HoloLif · Lifshitz holography: hydrodynamics and the large-D limit

Lifshitz holography: hydrodynamics and the large-D limit

The gauge/gravity duality (also known as holography) states that strongly interacting systems have a weakly coupled description in terms of classical gravity in one dimension higher and thus has been a very powerful tool in investigating the dynamics of strongly coupled quantum states of matter (such as high-temperature superconductors and the Quark-Gluon plasma) that are not amenable to analysis using conventional perturbative techniques or lattice simulations. The best understood realisation of the duality involves relativistic systems that are dual to gravitational physics in spacetimes that approach the so-called Anti-de-Sitter (AdS)spacetime asymptotically. The focus of this proposal is on a much subtler and less well-understood version of the duality, namely non-relativistic holography. Specifically, the proposed research focuses on holographic models that describe strongly coupled theories that admit Lifshitz symmetry: these are characterised by an anisotropic scaling of space and time and are thus intrinsically non-relativistic. The main aim of this action is to make progress on understanding non-relativistic holography better as well as exploring the properties of strongly coupled Lifshitz systems. This is achieved by studying gravitational quasinormal modes (QNMs). QNMs are damped oscillation modes and are particularly important in holography because they contain information about black hole dynamics in the sense of characterising the dissipation of the perturbed horizon. In this project we have calculate the gravitational QNMs for 2 distinct models that they give rise to Lifshitz dynamics. We found significant differences between the two models in terms of dissipation. Comparing our results with the already developed Lifshitz hydrodynamics, these results may have implications regarding the viability of one of the models for real-world systems. We also made progress on the radius of convergence of hydrodynamics and the phenomenon of pole-skipping from systems with charge in AdS, which is relevant for the 2 models of interest given also carry charge and was necessary for building intuition. To understand the origin of these differences in terms of dissipation on the gravity side of the duality, we took a step back and developed a framework for analytically extracting the hydrodynamic modes from the black hole horizon in asymptotically AdS spacetimes with the view of applying this to the Lifshitz case in the sequence. Along the way we have also fleshed out other connections between fluids and gravity, including gravitational turbulence and superfluid lattices.

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