Holographic axion model: A simple gravitational tool for quantum matter

Abstract

This is a complete and exhaustive review on the so-called holographic axion model-a bottom-up holographic system characterized by the presence of a set of shift symmetric scalar bulk fields whose profiles are taken to be linear in the spatial coordinates. This simple model implements the breaking of translational invariance of the dual field theory by retaining the homogeneity of the background geometry and therefore allowing for controllable and fast computations. The usages of this model are very vast and they are a proof of the spectacular versatility of the framework. In this review, we touch upon all the up-to-date aspects of this model from its connection with massive gravity and effective field theories, to its role in modeling momentum dissipation and elastic properties ending with all the phenomenological features and its hydrodynamic description. In summary, this is a complete guide to one of the most used models in Applied Holography and a must-read for any researcher entering this field.

Bound of diffusion constants from pole-skipping points: spontaneous symmetry breaking and magnetic field

“…Thus previous holographic studies of SSB [59][60][61][62][63][64][65][66][67][68] might be explained within this general analysis.…”

Holographic phonons by gauge-axion coupling

“…In the small frequency and momentum regime, our model shares the same hydrodynamic formulas with other holographic axion models [34] or the homogeneous models with more complicated setups [72,78] (even though the coefficients and parameters in the hydrodynamic formulation depend on the setup). This again verifies the statement that hydrodynamics provides a universal description for strongly coupled systems.…”

“…Better yet, one can easily realize explicit breaking (ESB) or spontaneous breaking (SSB) of translations differently by slightly changing the kinetic term of the axions in the bulk [30][31][32][33]. 1 For a comprehensive review on the holographic axion models, one refers to [34].…”

What’s inside a hairy black hole in massive gravity?

“…(2.1) corresponds to different boundary field theories. In particular, the shape of the potential and its behaviour near the AdS boundary at r = 0 determines whether translational invariance is broken explicitly or spontaneously in the dual field theory picture [31,35]. In the present work, we are interested in the following two cases:…”

“…The usages of this class of models in the Holographic community are very vast, specially in view of the applications to strongly coupled matter [27][28][29][30]. We refer the Reader to [31] for a complete and exhaustive review on the topic.…”