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.