Sum rules from an extra dimension

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.

Section: Jhep12(2017)156supporting

confidence: 91%

“…This is consistent with the conventions used in [2][3][4] . Note that the retarded correlator differs from that used in [1] by a sign.…”

Section: Sum Rulessupporting

confidence: 88%

“…We are interested in sum rules corresponding to the retarded correlator of the T xy component of the stress tensor in general d dimensions [2][3][4]. The retarded correlator is defined as…”

Section: Sum Rulesmentioning

confidence: 99%

Section: Jhep12(2017)156mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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