A bound on the speed of sound from holography

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.

Figures (1)

• Figure 1: Plot of the high-temperature approximation to $v_s^2$ in Eqs. (\ref{['vs2_result']}) and (\ref{['TfromPhiH']}) for $\Delta=3$ (solid line) versus a numerical solution (dashed line) for $v_s^2$ found using the methods of Ref. GubserNellore. The numerical solution is for $V(\phi) = -\frac{12}{L^2} \cosh(\frac{1}{2}\phi)$, which corresponds to $\Delta=3$ . The sound bound $v_s^{2}=1/3$ is shown as a horizontal dot-dashed line.