Transport coefficients in AdS/CFT and quantum gravity corrections due to a functional measure

TL;DR

This paper investigates how a functional measure affects transport coefficients in AdS/CFT, revealing certain quantities remain unchanged while others gain quantum corrections, indicating potential experimental tests with quark-gluon plasma.

Contribution

It demonstrates that some hydrodynamic transport coefficients are unaffected by the functional measure, while others receive significant quantum corrections, including imaginary parts indicating instability.

Findings

Shear viscosity and entropy density are unaffected by the functional measure.

Energy density and pressure receive significant quantum corrections.

Quantum corrections introduce imaginary parts, indicating instability in the boundary fluid.

Abstract

The presence of a functional measure is scrutinized on both sides of the dual gauge/gravity correspondence. Corrections to the transport coefficients in relativistic hydrodynamics are obtained using the linear response procedure. In particular, using first-order hydrodynamics, the shear viscosity, entropy density, diffusion constant, and speed of sound are shown not to acquire any corrections from the functional measure of gravity, for a Minkowski background metric. On the other hand, the energy density, the pressure, the relaxation time, the bulk viscosity, the decay rate of sound waves, and coefficients of conformal traceless tensor fields, are shown to carry significant quantum corrections due to the functional measure, even for a flat background. They all acquire an imaginary part that reflects the instability of the strongly-coupled fluids on the boundary CFT. This opens up the possibility of testing quantum gravity with the quark-gluon plasma.