High Energy Physics

Particle physics theory, phenomenology, and experiments

Includes:High Energy Physics - Theory(hep-th)High Energy Physics - Phenomenology(hep-ph)High Energy Physics - Experiment(hep-ex)High Energy Physics - Lattice(hep-lat)

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Integrable Systems

These notes are based on lecture courses I gave to third year mathematics students at Cambridge. They could form a basis of an elementary one--term lecture course on integrable systems covering the Arnold-Liouville theorem, inverse scattering transform, Hamiltonian methods in soliton theory and Lie point symmetries. No knowledge beyond basic calculus and ordinary differential equation is assumed.

2601.04077

Jan 2026High Energy Physics - Theory

Black hole thermodynamics at null infinity. Part 2: Open systems, Markovian dynamics and work extraction from non-rotating black holes

Black hole thermodynamics provides a unique setting in which general relativity, quantum field theory, and statistical mechanics converge. In semiclassical gravity, this interplay culminates in the generalized second law (GSL), whose modern proofs rely on information theoretic techniques applied to algebras of observables defined on null hypersurfaces. These proofs exhibit close structural parallels with the thermodynamics of open quantum systems governed by Markovian dynamics. In this work, we draw parallels between the dynamics of quantum fields in regions bounded by non expanding causal horizons and the thermodynamics of quantum systems weakly coupled to equilibrium reservoirs. We introduce a dictionary relating late time boundary conditions to the choice of reservoir, vacuum states to fixed points of the dynamics, and modular Hamiltonians to thermodynamic potentials. Building on results from a companion paper on dual generalized second laws at future null infinity, we show that additional terms appearing in the associated thermodynamic potentials admit a natural interpretation as work contributions. We demonstrate that certain non thermal vacuum states at null infinity allow for the operation of autonomous thermal engines and enable work extraction from the radiation. Extending the analysis to the Unruh vacuum in Schwarzschild and Kerr backgrounds, we obtain generalized grand potential type laws incorporating grey body effects and angular momentum fluxes. Altogether, our results clarify the thermodynamic description of black hole dynamics and place it within the broader framework of open quantum thermodynamics.

2601.03356

Jan 2026High Energy Physics - Theory

$2+2=4$

Motivated by the observation that $2+2=4$, we consider four-dimensional $\mathcal{N}=2$ superconformal field theories on $S^2\timesΣ$, turning on a suitable rigid supergravity background. On the one hand, reduction of a four-dimensional theory ${T}$ on a Riemann surface $Σ$ leads to a family $\mathscr{F}[{T}, Σ]$ of two-dimensional $(2,2)$ unitary SCFTs, a two-dimensional analog of the four-dimensional theories of class $\mathscr{S}$. On the other hand, reduction on $S^2$ yields a non-unitary two-dimensional CFT $\mathscr{C}[{T}]$ whose chiral algebra is the same as the one associated to ${T}$ by the standard SCFT/VOA correspondence. This construction upgrades the vertex operator algebra to a full-fledged two-dimensional CFT. What's more, it leads to a novel 2d/2d correspondence, a "$2+2 = 4$" analog of the "$4+2=6$" AGT correspondence: the $S^2$ partition function of $\mathscr{F}[{T}; Σ]$ is computed by correlation functions of $\mathscr{C}[{T}]$ on $Σ$. The elliptic genus of $\mathscr{F}[{T}; Σ]$ is instead computed by a topological QFT $\mathscr{E}[T]$ on $Σ$. A central question is whether one can give a purely two-dimensional presentation of the family $\mathscr{F}[{T}; Σ]$ of $(2, 2)$ theories. We propose an algorithm to realize the $(2, 2)$ theories as gauged linear sigma models when ${T}$ is an Argyres-Douglas theory of type $(A_1, A_{2k})$ and $Σ$ an $n$-punctured sphere. We perform stringent checks of our conjecture for $k=1$ and $k=2$.

2601.00058

Dec 2025High Energy Physics - Theory

2601.00605

Effective field theory for dissipative photons from higher-form symmetries

Recent developments in generalized symmetries have provided new insights into quantum field theories. Within this framework, photons can be understood as Nambu-Goldstone modes associated with a spontaneously broken higher-form symmetry. In this work, we develop an effective field theory that builds on this symmetry structure to describe the real-time dynamics of photons in insulating media at finite temperature. Combining the Schwinger-Keldysh formalism with the generalized coset construction, we formulate a symmetry-based effective action that incorporates both conservative and dissipative effects. The effective theory implements the dynamical Kubo-Martin-Schwinger symmetry, ensuring consistency with the fluctuation-dissipation relation and Onsager's reciprocal relations. Within this framework, we derive the entropy current associated with dissipative photon dynamics and demonstrate the non-negativity of its divergence, in accordance with the second law of thermodynamics. We also clarify the symmetry origin of the gauge redundancy in the unbroken phase within the Schwinger-Keldysh framework, relating it to strong and weak realizations of higher-form symmetries. Our results provide a model-independent effective description of photon dynamics in insulating media at finite temperature.

2601.00605

Jan 2026High Energy Physics - Theory

Qubits and Vacuum Amplitudes

High-energy colliders, such as the Large Hadron Collider (LHC) at CERN, are genuine quantum machines, so, in line with Richard Feynman's original motivation for Quantum Computing, the scattering processes that take place there are natural candidates to be simulated on a quantum system. Potential applications range from quantum machine learning methods for collider data analysis, to faster and more precise evaluations of intricate multiloop Feynman diagrams, more efficient jet clustering, improved simulations of parton showers, and many other tasks. In this work, the focus will be on two specific applications: first, the identification of the causal structure of multiloop vacuum amplitudes, a key ingredient of the Loop-Tree Duality and an area with deep connections to graph theory; and second, the integration and sampling of high-dimensional functions. The latter constitutes a first step toward the realization of a fully fledged quantum event generator operating at high perturbative orders.

2601.00722

Jan 2026High Energy Physics - Phenomenology

Diagnosing Critical Behavior in AdS Einstein-Maxwell-Scalar Theory via Holographic Entanglement Measures

We investigate the holographic mixed-state entanglement measures in the Einstein-Maxwell-Scalar (EMS) theory. Several quantities are computed, including the holographic entanglement entropy (HEE), mutual information (MI), entanglement wedge cross-section (EWCS), and butterfly velocity ($v_B$). Our findings demonstrate that these measures can effectively diagnose phase transitions. Notably, EWCS and MI, as mixed-state entanglement measures, exhibit behavior opposite to that of the HEE. Additionally, we study the butterfly velocity, a dynamic quantum information measure, and observe that it behaves differently from the static quantum information measures. We propose that the butterfly velocity is initially dominated by entanglement and subsequently by thermal entropy as the coupling constant increases. Moreover, we examine the scaling behavior of the holographic entanglement measures and find that all the critical exponents are equal to $1$, which is twice that of the scalar field. We also explore the inequality between EWCS and MI, noting that the growth rate of MI consistently exceeds that of EWCS during phase transitions. These features are expected to be universal across thermodynamic phase transitions, with the inequalities becoming more significant as one moves away from the critical point.

2601.00069

Dec 2025High Energy Physics - Theory

2601.00662

Extended BMS representations and strings

We construct in detail the irreducible representations of the BMS group with super rotations in three and four dimensions that have the same rest frame momenta as the massive and massless Poincare point particles. We compare these representations to those of the Poincare group and also to the analogous representations of global BMS. We argue that these extended BMS representations are carried by a string rather than a point particle. The super rotations play a crucial role in our discussions.

2601.00662

Jan 2026High Energy Physics - Theory

The JLMS formula in a large code with approximate error correction

Gauge/gravity duality is often described as a quantum error correcting code. However, as seen in the Jafferis-Lewkowycz-Maldacena-Suh (JLMS) formula, exact quantum error correction with complementary recovery (and thus entanglement wedge reconstruction) emerges only in the limit $G \to 0$. As a result, precise arguments controlling error terms have focused on what we call `small' codes which, as $G \to 0$, describe only perturbative excitations near a given classical solution. Such settings are quite restrictive and, in particular, they prohibit discussion of any modular flow that would change the classical background. As a result, they forbid consideration of modular flows generated by semiclassical bulk states at order-one modular parameters. In contrast, we present a single `large' code for the bulk theory that can accommodate such flows and, in particular, in the $G \to 0$ limit includes superpositions of states associated with distinct classical backgrounds. This large code is assembled from small codes that each satisfy an approximate Faulkner-Lewkowycz-Maldacena formula. In this extended setting we clarify the meaning of the (approximate) JLMS relation between bulk and boundary modular Hamiltonians and quantify its validity in an appropriate class of states.

2601.004421

Jan 2026High Energy Physics - Theory

Introduction to black hole thermodynamics

These are the lecture notes for a course at the "Roberto Salmeron School in Mathematical Physics" held at the University of Brasilia in September 2025, to be published in the proceedings book "Modern topics in mathematical physics." The course provides a concise and biased introduction to black hole thermodynamics. It covers the laws of black hole mechanics, Hawking radiation, Euclidean quantum gravity methods, and AdS black holes.

2512.24929

Dec 2025High Energy Physics - Theory

Correlators are simpler than wavefunctions

Several recent works have revealed a simplicity in equal-time correlators that is absent in their wavefunction counterparts. In this letter, we show that this arises from the simple fact that the correlator is obtained by integrating Feynman propagators over the full spacetime, as opposed to the half-space for the wavefunction. Several striking new properties of correlators for any graph are made obvious from this picture. Certain patterns of poles that appear in the wavefunction do not appear in the correlator. The correlator also enjoys several remarkable factorization properties in various limits. Most strikingly, the correlator admits a systematic Laurent expansion in the neighborhood of every pole, with the first subleading term vanishing for every pole. There is an especially simple understanding of the expansion around the total energy pole up to second order, given by a differential operator acting on the amplitude. Finally, we show how these results extend beyond single graphs to the full correlator in Tr $φ^3$ theory.

2512.237951

Dec 2025High Energy Physics - Theory

Sommerfeld Enhancement from Background Force and the Galactic Center GeV Excess

We study the impact of background-induced forces on dark matter (DM) annihilation and their implications for indirect detection. In the presence of a finite number density of background particles, loop-level interactions can generate an effective force that is significantly enhanced relative to the vacuum case. We construct a two-component DM model in which the dominant component is a fermionic particle $χ$ and the subdominant component is an ultralight pseudoscalar particle $φ$. The annihilation of $χ$ proceeds through the p-wave channel and produces gamma-ray emission. The finite density of $φ$ particles induces a background-enhanced force between $χ$ particles, leading to a sizable Sommerfeld enhancement of the annihilation. We show that a viable region of parameter space in this model can account for the gamma-ray excess observed in the Galactic Center using Fermi-LAT data. The background-induced force substantially amplifies the Sommerfeld enhancement and thus enlarges the parameter space capable of explaining the excess, highlighting the importance of background effects in astrophysical environments.

2512.24188

Dec 2025High Energy Physics - Phenomenology

Energy correlators in four-dimensional gravity

We investigate energy correlators in four-dimensional gravitational theories, which provide a simple class of infrared-finite observables. We compute the one- and two-point energy correlators at one loop in $\mathcal{N}=8$ supergravity and in pure Einstein gravity, with particular emphasis on the contact terms arising from the interplay between virtual corrections and real emissions. We explicitly demonstrate the cancellation of infrared divergences and verify the Ward identities associated with energy-momentum conservation. In the back-to-back limit, we derive an all-order expression for the energy-energy correlator, showing that it is governed by universal soft-graviton dynamics. We further introduce a particularly simple beam-averaged energy-energy correlator and compute it in different gravitational theories, including tree-level string theory. The resulting correlators exhibit analyticity and polynomial boundedness, allowing for the formulation of dispersion relations, which we explore. Finally, we discuss additional singularities of the gravitational energy correlators, absent in QCD, that originate from the long-range nature of the gravitational interactions.

2512.23791

Dec 2025High Energy Physics - Theory

Quantum dynamics of perfect fluids

We study the quantum field theory of zero temperature perfect fluids. Such systems are defined by quantizing a classical field theory of scalar fields $φ^I$ that act as Lagrange coordinates on an internal spatial manifold of fluid configurations. Invariance under volume preserving diffeomorphisms acting on these scalars implies that the long-wavelength spectrum contains vortex (transverse modes) with exact $ω_T=0$ dispersion relation. As a result, physically interpreting the perturbative quantization of this theory by standard methods has proven to be challenging. In this paper, we show that correlators evaluated in the class of semi-classical (Gaussian) initial states prepared at $t=0$ are well-defined and accessible via perturbation theory. The width of the initial state effectively acts as an infrared regulator without explicitly breaking diffeomorphism invariance. As an application, we compute stress tensor two-point correlators and show that vortex modes give a non-trivial contribution to the response function, non-local in both space and time.

2512.23793

Dec 2025High Energy Physics - Theory

Generalized Level-Rank Duality, Holomorphic Conformal Field Theory, and Non-Invertible Anyon Condensation

We study the interplay between holomorphic conformal field theory and dualities of 3D topological quantum field theories generalizing the paradigm of level-rank duality. A holomorphic conformal field theory with a Kac-Moody subalgebra implies a topological interface between Chern-Simons gauge theories. Upon condensing a suitable set of anyons, such an interface yields a duality between topological field theories. We illustrate this idea using the $c=24$ holomorphic theories classified by Schellekens, which leads to a list of novel sporadic dualities. Some of these dualities necessarily involve condensation of anyons with non-abelian statistics, i.e. gauging non-invertible one-form global symmetries. Several of the examples we discover generalize from $c=24$ to an infinite series. This includes the fact that Spin$(n^{2})_{2}$ is dual to a twisted dihedral group gauge theory. Finally, if $-1$ is a quadratic residue modulo $k$, we deduce the existence of a sequence of holomorphic CFTs at central charge $c=2(k-1)$ with fusion category symmetry given by $\mathrm{Spin}(k)_{2}$ or equivalently, the $\mathbb{Z}_{2}$-equivariantization of a Tambara-Yamagami fusion category.

2512.24419

Dec 2025High Energy Physics - Theory

2512.25005

Grassmannian Geometries for Non-Planar On-Shell Diagrams

On-shell diagrams are gauge invariant quantities which play an important role in the description of scattering amplitudes. Based on the principles of generalized unitarity, they are given by products of elementary three-point amplitudes where the kinematics of internal on-shell legs are determined by cut conditions. In the ${\cal N}=4$ Super Yang-Mills (SYM) theory, the dual formulation for on-shell diagrams produces the same quantities as canonical forms on the Grassmannian $G(k,n)$. Most of the work in this direction has been devoted to the planar diagrams, which dominate in the large $N$ limit of gauge theories. On the mathematical side, planar on-shell diagrams correspond to cells of the positive Grassmannian $G_+(k,n)$ which have been very extensively studied in the literature in the past 20 years. In this paper, we focus on the non-planar on-shell diagrams which are relevant at finite $N$. In particular, we use the triplet formulation of Maximal-Helicity-Violating (MHV) on-shell diagrams to obtain certain regions in the Grassmannian $G(2,n)$. These regions are unions of positive Grassmannians with different orderings (referred to as oriented regions). We explore the features of these unions, and show that they are pseudo-positive geometries, in contrast to positive geometry of a single oriented region. For all non-planar diagrams which are \emph{internally planar} there always exists a strongly connected geometry, and for those that are \emph{irreducible}, there exists a geometry with no spurious facets. We also prove that the already known identity moves, square and sphere moves, form the complete set of identity moves for all MHV on-shell diagrams.

2512.25005

Dec 2025High Energy Physics - Theory

2512.19370

From $\mathrm{d} \! \log$ to $\mathrm{d} \mathcal{E}$: Canonical Elliptic Integrands and Modular Symbol Letters with Pure eMPLs

We propose '$\mathrm{d} \mathcal{E}$-forms' as fundamental building blocks of canonical integrands for elliptic Feynman integrals, which lead to Kronecker-Eisenstein $ω$-form symbol letters. Built upon pure elliptic multiple polylogarithms, they provide a natural extension of the '$\mathrm{d} \! \log$-form' integrands and $\mathrm{d} \! \log$ letters for polylogarithmic cases. By introducing an extended basis treating all marked points equally, we manifest a hidden symmetry structure in the canonical connection matrix, and demonstrate its covariance under modular transformations. Our result provides a novel perspective on describing canonical bases and symbol letters in a unified language of pure functions.

2512.19370

Dec 2025High Energy Physics - Theory

Holographic Tensor Networks as Tessellations of Geometry

Holographic tensor networks serve as toy models for the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, capturing many of its essential features in a concrete manner. However, existing holographic tensor network models remain far from a complete theory of quantum gravity. A key obstacle is their discrete structure, which only approximates the semi-classical geometry of gravity in a qualitative sense. In \cite{Lin:2024dho}, it was shown that a network of partial-entanglement-entropy (PEE) threads, which are bulk geodesics with a specific density distribution, generates a perfect tessellation of AdS space. Moreover, such PEE-network tessellations can be constructed for more general geometries using the Crofton formula. In this paper, we assign a quantum state to each vertex in the PEE network and develop two holographic tensor network models: the factorized PEE tensor network, which takes the form of a tensor product of EPR pairs, and the random PEE tensor network. In both models we reproduce the exact Ryu-Takayanagi formula by showing that the minimal number of cuts along a homologous surface in the network exactly computes the area of this surface.

2512.19452

Dec 2025High Energy Physics - Theory

Higher lattice gauge theory from representations of 2-groups and 3+1D topological phases

We construct a higher lattice gauge theory based on the representation of 2-groups described by a category of crossed modules on a lattice model described by path 2-groupoids. Using these lattice gauge representations, an exactly solvable Hamiltonian for topological phases in 3+1 dimensions is constructed. We show that the ground states of this model are topological observables.

2512.19608

Dec 2025High Energy Physics - Lattice

Exotic Branes and Symmetries of String Theory

Are duality transformations symmetries of string theory? For AdS space-time the answer is no for generic asymptotic values of the moduli, since the duality symmetry is broken explicitly in the dual conformal field theory. In contrast, in string theory in flat space-time, monodromy around codimension two exotic branes show that duality transformations are spontaneously broken discrete gauge symmetries with observable consequences, provided macroscopic loops of these branes are not hidden behind an event horizon. We discuss how this can be achieved and how the situation in flat space-time differs from that in AdS space-time. We also discuss observability of codimension two non-BPS branes and codimension one BPS and non-BPS branes.

2512.19068

Dec 2025High Energy Physics - Theory

2512.19498

Six-loop gravitational interactions at the sixth post-Newtonian order

We compute the gravitational interaction of two coalescing compact objects at sixth post-Newtonian order in the static limit, employing the diagrammatic approach within the effective field theory framework of General Relativity. The calculation requires the evaluation of six-loop Feynman diagrams that are mapped onto two-point integrals with a gauge-theory-like structure, which are computed here for the first time. The resulting seventh-order contribution in Newton's constant is finite in three space dimensions. This result provides the most technically demanding missing ingredient for the determination of the conservative dynamics of the gravitational two-body system at sixth post-Newtonian order.

2512.19498

Dec 2025High Energy Physics - Theory

31,898 papers

2601.04162

2d Conformal Field Theories on Magic Triangle

The magic triangle due to Cvitanović and Deligne--Gross is an extension of the Freudenthal--Tits magic square of semisimple Lie algebras. In this paper, we identify all 2d rational conformal field theories associated to the magic triangle. These include various Wess--Zumino--Witten (WZW) models, Virasoro minimal models, compact bosons and their non-diagonal modular invariants. At level one, we find a two-parameter family of modular linear differential equation of fourth order whose solutions produce the affine characters of all elements in the magic triangle. We find a universal coset relation for the whole triangle which generalizes the dual pairs with respect to $(E_8)_1$ in the Cvitanović--Deligne exceptional series. This leads to the dimension and degeneracy of each primary field and also to five atomic models which constitute all theories in the triangle. At level two, we find a special row of the triangle -- the subexceptional series has novel $N=1$ supersymmetry, and the Neveu--Schwarz/Ramond characters satisfy a one-parameter family of fermionic modular linear differential equations. Moreover, we find many new coset constructions involving WZW models at higher levels.

2601.04162Jan 2026

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Three-particle scattering amplitudes from lattice QCD

I review recent progress in calculating scattering amplitudes and resonance properties involving three particles using results from lattice QCD. The necessary input is the finite-volume spectrum, and the outputs -- via solutions of integral equations -- are scattering amplitudes that can be continued into the complex plane to search for resonance poles. I describe the outlook for future extensions and applications of this work.

2601.04147Jan 2026

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Complete NLO BFKL impact factors for quarkonium hadroproduction in NRQCD: the case of ${}^1S_0^{[1]}$, ${}^1S_0^{[8]}$, and ${}^3S_1^{[8]}$ states

We present the first complete next-to-leading order calculation of the impact factors for hadroproduction of $S$-wave quarkonium states within the BFKL formalism. We present the computation of the real-emission contributions which completes the recent one of one-loop virtual corrections by one of us for the impact factors for the ${}^1S_0^{[1]}$, ${}^1S_0^{[8]}$, and ${}^3S_1^{[8]}$ NRQCD states. We prove the cancellation of soft divergences between real and virtual contributions, and that the surviving collinear singularities are compatible with factorisation up to one loop for a novel class of processes where BFKL resummation can be applied. Our work indeed represents the first complete NLO quarkonium impact factor in the BFKL framework and paves the way to first next-to-leading-logarithmic-precision studies for hadroproduction of forward-backward quarkonium associated production at hadron colliders.

2601.04142Jan 2026

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Freelance Fluid/Gravity Correspondence, 3d Analysis

Freelance holography program is an extension of gauge/gravity correspondence, where the gravity theory is defined on a portion of AdS with an arbitrary timelike boundary, with any desired boundary conditions. It is also known that gauge/gravity correspondence admits a fluid/gravity correspondence limit, where the gauge theory side is well described by a fluid. In this work, combining the two, we work through ``freelance fluid/gravity''. In particular, we study in detail the 2d fluid (3d Einstein gravity) case, where one has a good analytical control over the bulk equations due to their integrability and absence of viscosity in the 2d fluid. We study consistency and validity requirements for the freelance fluid/gravity and how the fluid changes along the renormalization group (RG) flow. We prove the $v_g$-theorem, stating that the group velocity of fluid waves $v_g$ is a decreasing function as we move toward the infrared region along the RG flow, regardless of the adopted boundary conditions. We also study examples of holographic fluid with various asymptotic boundary conditions.

2601.04115Jan 2026

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Effect of event classification on the Tsallis-thermometer

We analyze identified hadron spectra in pp collisions at $\sqrt{s} = 13$ TeV measured by ALICE within a non-extensive statistical framework. Spectra classified by multiplicity, flattenicity, and spherocity were fitted with the Tsallis-Pareto distribution, and the parameters were studied on the Tsallis-thermometer. Multiplicity and flattenicity classes follow a previously observed scaling, while the non-extensivity parameter shows a distinct sensitivity to the spherocity. A data-driven parametrization confirms a proportionality between the Tsallis temperature and mean transverse momentum, offering a simple estimate of the effective temperature. These results highlight the ability of the Tsallis-thermometer to capture both multiplicity and event-shape effects, linking soft and hard processes in small systems.

2601.04106Jan 2026

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Integrable Systems

2601.04077Jan 2026

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Renormalizable and unitary nonlocal quantum field theory with CPT violation and its implication

It is a common belief that any relativistic nonlocal quantum field theory encounters either the problem of renormalizability or unitarity or both of them. It is also known that any local relativistic quantum field theory (QFT) possesses the CPT symmetry. In this Letter we show that a previously proposed nonlocal Lorentz invariant QFT, which violates the CPT theorem, is both renormalizable and unitary, thus being a first presented example in the literature of such a nonlocal theory. The theory satisfies the requirement of causality as well. A further generalization of such a nonlocal QFT to include the gauge theories is also envisaged. In particular, dressing such a Standard Model with a CP violating phase, will make the theory satisfying most of the necessary criteria to finally explain the baryon asymmetry of the universe by a viable QFT. As for the necessity of baryon number violation, there are hopefully several possibilities such as by GUT and electroweak baryogenesis, leptogenesis or sphalerons.

2601.04037Jan 2026

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Axion Masses as an Inevitable Consequence of Supersymmetry Breaking

We investigate a supersymmetric framework in which soft supersymmetry-breaking effects provide the dominant origin of Peccei--Quinn (PQ) symmetry breaking and axion mass generation. In the supersymmetric limit the theory possesses an exact PQ symmetry and a massless axion, while the inclusion of soft terms proportional to the gravitino mass induces spontaneous PQ breaking, stabilizes the saxion direction, and generates a mass for the axion. As a consequence, the axion, saxion, and axino masses are all controlled by the supersymmetry-breaking scale, leading to a correlated and predictive spectrum of axion-like states. The presence of explicit soft PQ-breaking terms raises the question of vacuum alignment and CP violation. We show that although the axion mass does not originate from QCD instantons, the induced strong CP phase is parametrically suppressed by the hierarchy between the QCD-induced and soft-induced axion masses. As a result, the explicit breaking does not generate an observable CP-violating vacuum angle across the parameter space of interest. We analyze the phenomenological implications of this scenario, including axion lifetimes, axion--photon couplings, and laboratory, astrophysical, and cosmological constraints. Direct confrontations with beam-dump and collider searches, together with Big Bang nucleosynthesis bounds, demonstrate that a substantial region of parameter space remains viable and testable. The framework thus provides a self-consistent and phenomenologically rich realization of axion-like particles whose masses arise predominantly from soft supersymmetry breaking.

2601.04017Jan 2026

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Chern-Simons-like formulation of 3D MMG-like massive gravity models

We investigate the Chern-Simons-like formulation of 3D MMG-like massive gravity models that are "third-way consistent". Building on previous work on exotic massive gravities, we analyze a class of MMG-like theories characterized by a specific parity structure and an auxiliary field hierarchy. Focusing on the simplest non-trivial case, we solve the full set of field equations, determine the AdS background solutions, compute the central charges of the dual CFT, and perform a linearized analysis to obtain the mass spectrum. Along the chiral line, the linearized mass operator develops a rank-2 Jordan block, signaling logarithmic behavior of massive modes in the dual two-dimensional CFT. At a special degenerate point, this structure is enhanced to a rank-3 Jordan block, giving rise to two logarithmic partners and an ultra-logarithmic sector in the boundary theory.

2601.03936Jan 2026

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Beyond Form Factors: Precise Angular Tests in Hadronic $τ$ Decays

Semileptonic $τ$ decays mainly proceed via interactions between charged lepton and quark currents. The hadronization of the quark current is intrinsically nonperturbative and generally cannot be addressed analytically. In these proceedings, we propose using symmetry arguments alone to construct clean angular observables, which, within the Standard Model and in the absence of long-distance electromagnetic corrections, remain form-factor independent. These predictions can be experimentally tested, and any observed deviation could signal either effects of physics beyond the Standard Model or provide a clean benchmark for long-distance electromagnetic corrections. We also perform a first estimate of the expected impact of new physics in an EFT framework.

2601.03912Jan 2026

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2601.03879

Defects in N=1 minimal models and RG flows

Utilising the symmetry constraints of suitable topological defects, the possible RG flows of N=1 superconformal minimal models are studied. We first employ a coset description that only captures the bosonic subalgebra, and then generalise the discussion to the actual superconformal models.

2601.03879Jan 2026

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Phases of the $q$-deformed $\mathrm{SU}(N)$ Yang-Mills theory at large $N$

We investigate the $(2+1)$-dimensional $q$-deformed $\mathrm{SU}(N)_k$ Yang-Mills theory in the lattice Hamiltonian formalism, which is characterized by three parameters: the number of colors $N$, the coupling constant $g$, and the level $k$. By treating these as tunable parameters, we explore how key properties of the theory, such as confinement and topological order, emerge in different regimes. Employing a variational mean-field analysis that interpolates between the strong- and weak-coupling regimes, we determine the large-$N$ phase structure in terms of the 't Hooft coupling $λ_\mathrm{tH}=g^2N$ and the ratio $k/N$. We find that the topologically ordered phase remains robust at large $N$ under appropriate scalings of these parameters. This result indicates that the continuum limit of large-$N$ gauge theory may be more intricate than naively expected, and motivates studies beyond the mean-field theory, both to achieve a further understanding of confinement in gauge theories and to guide quantum simulations of large-$N$ gauge theories.

2601.03843Jan 2026

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Topological quantization of vector meson anomalous couplings

We uncover a new anomalous term in hidden local symmetry that enforces the topological quantization of vector-meson anomalous couplings. Unlike existing formulations in the literature, which introduce several unquantized coefficients, our term removes this freedom by fixing the couplings to quantized, topologically determined values. We further conjecture that it saturates the anomaly, explaining the success of vector-meson dominance while pinpointing where saturation must fail. High-precision measurements of $η^{(\prime)}\toπ^+π^-γ^*$ form factors at BESIII and the Super $τ$-Charm Facility can provide a definitive experimental discriminator of this quantized picture.

2601.03740Jan 2026

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A glimpse into the Ultrametric spectrum

The non-relativistic string spectrum is built from integer-spaced energy quanta in such a way that the high-temperature asymptotics, via the Hardy-Ramanujan formula for integer partitions, reduces to standard two-dimensional thermodynamics. Here we explore deformed realizations of this behavior motivated by $p$-adic string theory and Lorentzian versions thereof with a non-trivial spectrum. We study the microstate scaling that results on associating quantum harmonic oscillators to the normal modes of tree-graphs rather than string graphs and observe that Hardy-Ramanujan scaling is not realized. But by computing the eigenvalues of the derivative operator on the $p$-adic circle and by determining the eigenspectrum of the Neumann-to-Dirichlet operator, we uncover a spectrum of exponentially growing energies but with exponentially growing degeneracies balanced in such a way that Hardy-Ramanujan scaling is realized, but modulated with log-periodic fluctuations.

2601.03738Jan 2026

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Scalar vacuum densities on Beltrami pseudosphere

We investigate the combined effects of spatial curvature and topology on the properties of the vacuum state for a charged scalar field localized on the (2+1)-dimensional Beltrami pseudosphere, assuming that the field obeys quasiperiodicity condition with constant phase. As important local characteristics of the vacuum state the vacuum expectation values (VEVs) of the field squared and energy-momentum tensor are evaluated. The contributions in the VEVs coming from geometry with an uncompactified azimuthal coordinate are divergent, whereas the compact counterparts are finite and are analysed both numerically and asymptotically. For small values of proper radius of the compactified dimension, the leading terms of topological contributions are independent of the field mass and curvature coupling parameter, increasing by a power-law. In the opposite limit, the VEVs decay following a power-law in the general case. In the special case of a conformally coupled massless field the behavior is different. Unlike the VEV of field squared and vacuum energy density, the radial and azimuthal stresses are increasing by absolute value. As a consequence, the effects of nontrivial topology are strong for the stresses in this case at small values of radial coordinate.

2601.03732Jan 2026

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Addicted to Flavour: 1976-2026

I describe my activities in Flavour Physics from 1976 to 2026. However, this 50th anniversary is not the only motivation for this writing. The second reason is the 350th anniversary of the discovery of the first animalcula by van Leeuvanhoek in 1676. Flavour physics makes it possible to search for new animalcula at distance scales far shorter than those resolved by van Leeuwenhoek in 1676 and even shorter than those directly accessible at the Large Hadron Collider. Achieving this goal requires not only precise measurements of a wide variety of processes, but also equally precise theoretical calculations, both within the Standard Model (SM) and beyond it. In this respect, next-to-leading-order (NLO) and next-to-next-to-leading-order (NNLO) QCD calculations of various Wilson coefficients in the SM and beyond it, in which I was involved for two decades, as well as reliable treatments of non-perturbative QCD effects, are indispensable. Equally important is the proper choice of observables that are best suited to revealing these new animalcula of particle physics. Moreover, in my view it is crucial to develop strategies for the search for New Physics (NP) that go beyond the global fits that are very popular today. While effective field theories such as WET and SMEFT are formulated in terms of Wilson coefficients of the relevant operators, with correlations characteristic of the SM and of specific NP scenarios, the most direct tests of the SM and its extensions are, in my opinion, correlations among different observables that are characteristic of particular new animalcula at work. Numerous colourful plots in this article illustrate this point. I hope that these ideas are clearly conveyed in my Flavour Autobiography, which also includes my memories of many conferences, workshops, and schools, as well as related anecdotes that are not always directly connected to physics.

2601.03722Jan 2026

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Chiral anomaly: from vacuum to Columbia plot

We use a low-energy effective approach, the extended linear sigma model, to study realizations of the $U(1)_A$ anomaly with different operators, linear and quadratic in the 't Hooft determinant. After discussing the parameterization in agreement with vacuum's phenomenology, we investigate the influence of these different anomaly terms on the Columbia plot: the square of the 't Hooft determinant favors a cross-over for small quark masses. Finally, we also discuss the extension of the 't Hooft determinant to cases in which different mesonic multiplets interact with each other. Novel chiral anomalous interaction terms involving excited (pseudo)scalar states, pseudovector, and pseudotensor mesons are expressed via a mathematical extension of the determinant, denoted as a polydeterminant.

2601.03710Jan 2026

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Why is the $Z_c(3900)$ absent in the $h_cπ$ final state?

In this work, we perform a comprehensive phenomenological analysis of the exotic hadronic states $Z_c(3900)$, $Z_c(4020)$, $Z_b(10610)$ and $Z_b(10650)$ within the framework of Heavy Quark Spin Symmetry (HQSS) and its violation. By constructing S-wave contact interactions between elastic ($D\bar{D}^*/D^*\bar{D}^*$ or $B\bar{B}^*/B^*\bar{B}^*$) and inelastic ($J/ψπ, h_cπ$ or $Υπ$, $h_bπ$) channels, we solve the Lippmann-Schwinger equation to obtain physical production amplitudes and perform a global fit to experimental invariant-mass spectra. Our results demonstrate a striking difference between the charm and bottom sectors: HQSS violation is negligible in the bottom system, leading to comparable peak structures for both $Z_b$ states in all hidden-bottom decay channels. In contrast, significant HQSS breaking is required to describe the $Z_c$ system, where the violation is predominantly concentrated in the elastic interactions. This explains the observed selectivity: $Z_c(3900)$ appears prominently only in $J/ψπ$, while $Z_c(4020)$ appears only in $h_cπ$. Pole analysis confirms the molecular nature of the states, with the $Z_c(4020)$ likely arising from a threshold cusp effect. The model's robustness is verified against variations of the form factor and cutoff, showing stable results.

2601.03697Jan 2026

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Role of $Σ(1660)$ in the $K^- p \toπ^0π^0Σ^0$ reaction

The processes of $K^-p \to π^0 π^0 Σ^0$ and $K^- p \to π^0 Λ(1405)$ are studied within the effective Lagrangian approach. In addition to the ``background" contribution from the $u$-channel nucleon pole term, contribution from the $Σ(1660)$ resonance with spin-parity $J^P=1/2^+$ is also considered. For the $K^-p \to π^0 π^0 Σ^0$ reaction, we perform a calculation for the total and differential cross sections by considering the contribution from the $Σ(1660)$ intermediate resonance decaying into $π^0 Λ(1405)$ with $Λ(1405)$ decaying into $π^0 Σ^0$. With our model parameters, the available experimental data on both the $K^-p \to π^0 π^0 Σ^0$ and $K^- p \to π^0 Λ(1405)$ reactions can be fairly well reproduced. It is shown that we really need the contribution from the $Σ(1660)$ resonance, and that these experimental measurements could be used to determine some properties of the $Σ(1660)$ resonance.

2601.03692Jan 2026

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2601.03631

Real-time Gravitational Wave Response in Thermal Spinning fields

We study how the spin content of the thermal plasmas affects the propagation of gravitational waves in a radiation-dominated universe. As a simple but representative setup, we consider conformal scalar, Weyl fermion, and Maxwell fields that provide the background radiation, and we ask whether the resulting damping and phase shift of gravitational waves retain any memory of their spins. We revisit this question in a real-time quantum-field-theoretic framework, where the stress tensor splits into a background part, a dynamical (history-dependent) response, and local contact terms, with an additional on-shell projection fixed by the Friedmann equation. We find that the dynamical spin-dependent response arises on a short time scale characterized by the radiation temperature, which is exactly canceled by the local responses. As a result, the remaining long-time response is universal and consistent with kinetic theory in the hard thermal limit. Although the underlying mechanism exhibits strong spin dependence, it leaves no observable imprint on the large-scale effective dynamics of gravitational waves in this setup.

2601.03631Jan 2026

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