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A bound on the speed of sound from holography · Around

2009

A bound on the speed of sound from holography

Cherman, Aleksey, Cohen, Thomas D., Nellore, Abhinav

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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.

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For some V ⁡ ( ϕ ) V(\phi) , there is a secondary high-temperature limit as V ⁡ ( ϕ H ) → ∞ V(\phi_{H})\rightarrow\infty . However, in all known cases, this limit occurs along an energetically unstable branch of s ⁡ ( T ) s(T) ( i.e

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In Ref. BuchelPagnuttiExotic v s 2 v_{s}^{2} was seen to exceed the conformal value in energetically unstable thermodynamic phases that somewhat exotically persist to arbitrarily high temperatures. However, the energetically stable phase in that system has v s 2 v_{s}^{2} bounded from above by the conformal value

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