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On the universal identity in second order hydrodynamics

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arxiv 1412.5685 v3 pith:3DOL4HCN submitted 2014-12-18 hep-th hep-ph

classification hep-thhep-ph
keywords orderactioncouplingdualidentitylambdasecondtheory
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We compute the 't Hooft coupling correction to the infinite coupling expression for the second order transport coefficient $\lambda_2$ in ${\cal N}=4$ $SU(N_c)$ supersymmetric Yang-Mills theory at finite temperature in the limit of infinite $N_c$, which originates from the $R^4$ terms in the low energy effective action of the dual type IIB string theory. Using this result, we show that the identity involving the three second order transport coefficients, $2 \eta \tau_\Pi - 4 \lambda_1 - \lambda_2 =0$, previously shown by Haack and Yarom to hold universally in relativistic conformal field theories with string dual descriptions to leading order in supergravity approximation, holds also at next to leading order in this theory. We also compute corrections to transport coefficients in a (hypothetical) strongly interacting conformal fluid arising from the generic curvature squared terms in the corresponding dual gravity action (in particular, Gauss-Bonnet action), and show that the identity holds to linear order in the higher-derivative couplings. We discuss potential implications of these results for the near-equilibrium entropy production rate at strong coupling.

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