Bound on the speed of sound from holography

We show that the squared speed of sound vs2 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 vs2 exceeds 1/3 in energetically favored configurations. We conjecture that vs2=1/3 represents an upper bound for a broad class of four-dimensional theories.