Shear sum rule in higher derivative gravity theories

Abstract

We study holographic shear sum rules in Einstein gravity with curvature squared corrections. Sum rules relate weighted integral over spectral densities of retarded correlators in the shear channel to the one point functions of the CFTs. The proportionality constant can be written in terms of the data of three point functions of the stress tensors of the CFT (t 2 and t 4 ). For CFTs dual to two derivative Einstein gravity, this proportionality constant is just d 2(d+1) . This has been verified by a direct holographic computation of the retarded correlator for Einstein gravity in AdS d+1 black hole background. We compute corrections to the holographic shear sum rule in presence of higher derivative corrections to the Einstein-Hilbert action. We find agreement between the sum rule obtained from a general CFT analysis and holographic computation for Gauss Bonnet theories in AdS 5 black hole background. We then generalize the sum rule for arbitrary curvature squared corrections to Einstein-Hilbert action in d ≥ 4. Evaluating the parameters t 2 and t 4 for the possible dual CFT in presence of such curvature corrections, we find an agreement with the general field theory derivation to leading order in coupling constants of the higher derivative terms.

The Conformal Bootstrap: Theory, Numerical Techniques, and Applications

“…Other generalizations of these bounds have been explored in Li et al (2016a), Komargodski et al (2017a), Chowdhury et al (2017a), Cordova et al (2017b), Meltzer and Perlmutter (2017), and Cordova and Diab (2018). Sum rules involving the same coefficients were also recently presented in Witczak-Krempa (2015), Chowdhury et al (2017b), Chowdhury (2017), and Gillioz et al (2017Gillioz et al ( , 2018.…”

Butterfly velocity in quadratic gravity

“…Above metric was first derived in [38]. It had been used by [38,39] to show the viscosity bound violation and shear sum rule in higher derivative gravity theories [46]. We will use this metric to study the effect of quadratic gravity on the butterfly velocity.…”

“…Holographic superconductors with higher curvature corrections had been extensively studied [43][44][45]. Holographic shear sum rule in Einstein gravity corrected by squared curvature was studied in [46]. The higher derivative terms are shown to have a strong impact on the bound on charge diffusion [47,48].…”