Anisotropic critical points from holography

TL;DR

This work develops a unifying, analytically controlled holographic framework for strongly coupled anisotropic matter via a five-dimensional EMDA model with exponential couplings. By constructing exact black-brane backgrounds sourced by axions, magnetic fields, and charge densities (individually and in combinations), the authors obtain up to three independent Lifshitz-like exponents and a hyperscaling violation exponent, with full analytic expressions for thermodynamics, stress-energy, and nonlocal probes. They derive the holographic EOS, anisotropic speeds of sound, butterfly velocities, and perform a comprehensive constraint analysis using NEC, thermodynamic stability, and causality, identifying broad regions of natural, physically viable couplings. Additionally, hard probes such as Brownian diffusion, Langevin dynamics, and jet quenching are computed analytically, revealing directional dependence and potential violations of isotropic bounds. The results provide robust benchmarks for anisotropic strongly coupled systems relevant to the quark-gluon plasma and dense QCD matter in astrophysical contexts, and they lay groundwork for RG-flow interpolations and QNM studies in anisotropic holography.

Abstract

We present a comprehensive analysis of generic 5-dimensional Einstein-Maxwell-Dilaton-Axion (EMDA) holographic theories with exponential couplings. We find and classify exact, analytic, anisotropic solutions, both zero-temperature vacua and finite-temperature black brane backgrounds, with anisotropy sourced by scalar axions, magnetic fields, and charge densities, that can be interpreted as IR fixed points of renormalisation-group flows from UV-conformal fixed points. The resulting backgrounds feature a hyperscaling violation exponent and up to three independent Lifshitz-like exponents, generated by an equal number of independent coupling constants in the EMDA action. We derive the holographic stress-energy tensor and the corresponding equation of state, and discuss the behavior of the anisotropic speed of sound and butterfly velocity. We show that these theories can be consistently constrained by imposing several natural requirements, including energy conditions, thermodynamic stability, and causality. Additionally, we analyse hard probes in this class of theories, including Brownian motion, momentum broadening and jet quenching, and we demonstrate that a fully analytic treatment is possible, making their dependence on the underlying anisotropy explicit. We highlight the relevance of these models as benchmarks for strongly coupled anisotropic matter in nature, from the quark-gluon plasma created in heavy-ion collisions to dense QCD phases in neutron-star mergers and the cores of compact objects.

Figures (10)

• Figure 1: Allowed parameter space for the couplings ${\left( {\gamma,\lambda,\sigma} \right)}$ in the case of a magnetic field parallel to the linear axion. The red shaded region represents the intersection of the NEC and thermodynamic stability constraints, while the transparent cyan subvolume highlights the additional requirement of a physically acceptable metric signature. The dense overlapping region indicates the physically viable subspace satisfying both conditions. Although the NEC and stability constraints do not exactly coincide with the signature condition, a substantial intersection exists. Imposing further physical constraints, such as those arising from butterfly velocity bounds, reduces the volume but leaves a sizable admissible region.
• Figure 2: Allowed parameter space for the couplings ${\left( {\gamma,\lambda,\sigma} \right)}$ in the case of a magnetic field transverse to the linear axion. The red shaded region represents the intersection of the NEC and thermodynamic stability constraints, while the transparent cyan subvolume corresponds to the additional requirement ensuring a physically acceptable metric signature. The overlapping dense region denotes the physically viable regime satisfying both conditions. The plot confirms that while the NEC and stability subvolumes overlap with the signature constraint region, they do not coincide exactly. A large subvolume of acceptable parameters persists. Further imposing constraints from physical observables, such as the butterfly velocity, reduces this volume but still leaves a nontrivial allowed region.
• Figure 3: The allowed volume of parameters ${\left( {\theta,z_1,z_3} \right)}$ for the magnetic field parallel to the axion charge density is the overlapping dense shaded area. The orange-shaded denser volume reflects to the NEC and the thermodynamic stability and the cyan-shaded volume consists of the positivity of the metric constants. Their overlap is the regime where all conditions are satisfied.
• Figure 4: The allowed volume of parameters ${\left( {\theta,z_2,z_3} \right)}$ for the magnetic field transverse to the axion charge density is the overlapping dense shaded area. The orange-shaded volume reflects to the NEC and the thermodynamic stability and the green-shaded volume consists of the positivity of the metric constants. Their overlap is the regime where all conditions are satisfied.
• Figure 5: Theories with magnetic field transverse to the axion charge density are characterised with the parametric coupling's space ${\left( {\gamma,\lambda,\sigma} \right)}$ plotted. Here we have imposed all the available conditions for natural theories, NEC, thermodynamic stability, physical butterfly velocity bounds. This is a subset of the volume presented in Figure \ref{['figure:a1']}.