What can gauge-gravity duality teach us about condensed matter physics?

TL;DR

This paper explores how gauge-gravity duality can provide new insights into complex condensed matter systems, including quantum critical points and exotic states, by offering computational tools for strongly-coupled regimes.

Contribution

It demonstrates the application of gauge-gravity duality to analyze conformal quantum matter and compressible quantum matter, highlighting its potential for understanding strongly-coupled condensed matter phenomena.

Findings

Gauge-gravity duality aids in computing low-frequency correlations at quantum critical points.

It offers a framework to understand exotic compressible quantum states.

The methods bridge condensed matter physics with gravitational theories.

Abstract

I discuss the impact of gauge-gravity duality on our understanding of two classes of systems: conformal quantum matter and compressible quantum matter. The first conformal class includes systems, such as the boson Hubbard model in two spatial dimensions, which display quantum critical points described by conformal field theories. Questions associated with non-zero temperature dynamics and transport are difficult to answer using conventional field theoretic methods. I argue that many of these can be addressed systematically using gauge-gravity duality, and discuss the prospects for reliable computation of low frequency correlations. Compressible quantum matter is characterized by the smooth dependence of the charge density, associated with a global U(1) symmetry, upon a chemical potential. Familiar examples are solids, superfluids, and Fermi liquids, but there are more exotic possibilities involving deconfined phases of gauge fields in the presence of Fermi surfaces. I survey the compressible systems studied using gauge-gravity duality, and discuss their relationship to the condensed matter classification of such states. The gravity methods offer hope of a deeper understanding of exotic and strongly-coupled compressible quantum states.