A bound on the speed of sound from holography

TL;DR

This paper establishes an upper bound of 1/3 for the squared speed of sound in certain strongly coupled four-dimensional field theories with gravity duals, suggesting a universal limit at high temperatures.

Contribution

It proves a theoretical upper bound on the speed of sound in a class of holographic field theories, extending understanding of their thermodynamic properties.

Findings

The squared speed of sound is bounded above by 1/3 at high temperatures.

No known theories with gravity duals exceed this bound.

The bound is conjectured to be universal for similar theories.

Abstract

We show that the squared speed of sound v_{s}^{2} is bounded from above at high temperatures by the conformal value of 1/3 in a class of strongly coupled four-dimensional field theories, given some mild technical assumptions. This class consists of field theories that have gravity duals sourced by a single scalar field. There are no known examples to date of field theories with gravity duals for which v_{s}^{2} exceeds 1/3 in energetically favored configurations. We conjecture that v_{s}^{2}=1/3 represents an upper bound for a broad class of four-dimensional theories.