Sound Velocity Bound and Neutron Stars

It has been conjectured that the velocity of sound in any medium is smaller than the velocity of light in vacuum divided by root 3. Simple arguments support this bound in nonrelativistic and/or weakly coupled theories. The bound has been demonstrated in several classes of strongly coupled theories with gravity duals and is saturated only in conformal theories. We point out that the existence of neutron stars with masses around two solar masses combined with the knowledge of the equation of state of hadronic matter at low densities is in strong tension with this bound.