SCFT deformations via uplifted solitons

TL;DR

The paper develops a general holographic mechanism to implement a supersymmetry-preserving deformation of 4d SCFTs by uplifting a supersymmetric AdS$_5$ soliton from minimal $d=5$ gauged supergravity to ten- and eleven-dimensional string/M-theory backgrounds. The resulting geometries realize twisted compactifications of the original SCFTs on a circle, yielding confining and gapped (2+1)-dimensional IR theories, with Supersymmetry preserved at a special parameter point. A comprehensive set of holographic observables—Wilson loops, ’t Hooft loops, entanglement entropy, flow central charge, holographic complexity, gauge couplings, and global symmetry breaking—exhibit universal confinement features across IIB, IIA, and M-theory uplifts for diverse internal manifolds (S^5, Y^{p,q}, AFPRT, GM, T^{1,1}, etc.). The construction applies broadly to any holographic solution that truncates to $d=5$ minimal gauged supergravity and can be extended to other AdS factors, providing a versatile framework for studying dimensional transmutation, confinement, and IR dynamics in strongly coupled QFTs.

Abstract

A holographic method for implementing a particular supersymmetry-preserving deformation to 4d SCFTs is presented. At the heart of the procedure is a soliton solution of minimal $d=5$ gauged supergravity. Embedding this solution into ten- and eleven-dimensional string theory backgrounds of the form AdS$_5 \times M$, we systematically construct a range of new solutions. Each holographically realizes a twisted compactification of the SCFT$_4$ dual to the original background. In the IR, the resulting SQFTs flow to gapped three-dimensional systems. Using a variety of holographic observables, we give evidence for this interpretation and for confinement in the deformed SQFTs. Our method applies to any holographic solutions admitting a consistent truncation to minimal $d=5$ gauged supergravity, and can likely be generalized to solutions with other AdS$_d$ factors.

Figures (4)

• Figure 1: Plots of the length and energy of separation of the quark-anti-quark system \ref{['L-Wilson']} as a function of the turning point of the string $r_0$, for the deformed $\mathrm{AdS}\times\mathrm{S}^5$ case. The parameters are fixed to $l=\mu=q=1$. We emphasize that the results depicted in these plots, as well as Figure \ref{['plotE(L)-Wilson']}, are the same for all the families of solutions we presented.
• Figure 2: Parametric plot of the energy \ref{['energy-Wilson']} with respect to the length of the separation of the pair for the deformed $\mathrm{AdS}\times\mathrm{S}^5$ with $l=\mu=q=1$. This interpolates between a Coulomb-like behaviour dictated by conformality and a linear behaviour for large values of $L$, signaling confinement.
• Figure 3: Plots of the length function, its approximate expression and the energy as a function of the length, for the monopole-anti-monopole pair for the 't Hooft loop, with $l=\mu=q=1$ fixed. We see the double-valuedness of the energy, which expresses screening as a phase transition.
• Figure 4: Plot of the flow central charge normalized to its $\mathrm{UV}$ value for the deformed $\mathrm{AdS}_5\times \mathrm{T}^{1,1}$ (keeping $l=\mu=q=1$): It interpolates between an IR gapped 3d system (expressing a $\mathrm{TQFT}$ in the deep IR) and the 4d $\mathrm{SCFTs}$ in the UV, where the value it takes depends on the details of the internal space of the theory. This behaviour is similar for all the supergravity solutions in this work.