Bound on the speed of sound from holography

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.