Shear viscosity in QFTs dual to AdS spherical black holes

Matteo Tuveri,Edgardo Franzin,Mariano Cadoni

doi:10.1088/1742-6596/942/1/012018

Matteo Tuveri, Edgardo Franzin + Show 1 more

Open Access

https://doi.org/10.1088/1742-6596/942/1/012018

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Abstract

In the framework of the AdS/CFT correspondence, we define and compute the spherical analogue of the shear viscosity for QFTs dual to five-dimensional charged AdS black holes in general relativity (GR) and Gauss-Bonnet (GB) gravity. We show that the ratio between this quantity and the entropy density, ῆ/s exhibits a temperature-dependent hysteresis.

Highlights

Nowadays, holography plays a central role in theoretical gravitational physics and has produced several successful applications as, for example, the AdS/CFT correspondence
It is well-known that the KSS bound is violated by higher curvature terms in the EinsteinHilbert action [7] or by breaking of translational or rotational symmetry of the black brane background [8,9,10,11,12]
It is still possible to define a relativistic hydrodynamics in curved spacetimes without translational symmetry as an expansion in the derivatives of the hydrodynamic fields of the stress-energy tensor [14] and a related Kubo formula for the shear viscosity

Summary

Introduction

Holography plays a central role in theoretical gravitational physics and has produced several successful applications as, for example, the AdS/CFT correspondence It gives insights on quantum gravity and it is a powerful tool for the description of phase transitions and the computation of transport coefficients in strongly coupled QFTs [1,2,3,4,5] in the hydrodynamic limit. To derive a Kubo formula for CFTs living on the boundary of AdS5, whose spatial section is the three-sphere, we consider small perturbations around the boundary background metric, i.e. gab = gab + hab. It is important to stress that, with respect to the planar case, we have an additional contribution to the stress-energy tensor (2) ruled by the transport coefficient κ This is rather expected in view of the breaking of translational invariance. Q for RN BHs) [27, 30], first-order one (controlled by T ) and metastabilities (small/large BH region separated by metastable region of intermediate BHs)

Linear perturbations

Conclusion