Holographic stress tensor at finite coupling

Abstract:We derive the universal terms of entanglement entropy for 6d CFTs by applying the holographic and the field theoretical approaches, respectively. Our formulas are conformal invariant and agree with the results of [37,38]. Remarkably, we find that the holographic and the field theoretical results match exactly for the C 2 and Ck 2 terms, where C and k denote the Weyl tensor and the extrinsic curvature, respectively. As for the k 4 terms, we meet the splitting problem of the conical metrics. The splitting problem in the bulk can be fixed by equations of motion. As for the splitting on the boundary, we assume the general forms and find that there indeed exists suitable splitting which can make the holographic and the field theoretical k 4 terms match. Since we have much more equations than the free parameters, the match for k 4 terms is non-trivial.

Section: Jhep10(2015)049mentioning

confidence: 99%

Universal terms of entanglement entropy for 6d CFTs

Miao

2015

“…It should be mentioned that Camps [20] also made important contributions in this direction. For recent developments of HEE, please refer to [21][22][23][24][25][26][27][28][29][30][31][32]. So far, HEE for gravitational actions which include derivatives of the curvature is not known.…”

Section: Jhep08(2015)031mentioning

confidence: 99%

Holographic entanglement entropy for the most general higher derivative gravity

Miao

Guo

2015

134

The holographic entanglement entropy for the most general higher derivative gravity is investigated. We find a new type of Wald entropy, which appears on entangling surface without the rotational symmetry and reduces to usual Wald entropy on Killing horizon. Furthermore, we obtain a formal formula of HEE for the most general higher derivative gravity and work it out exactly for some squashed cones. As an important application, we derive HEE for gravitational action with one derivative of the curvature when the extrinsic curvature vanishes. We also study some toy models with non-zero extrinsic curvature. We prove that our formula yields the correct universal term of entanglement entropy for 4d CFTs. Furthermore, we solve the puzzle raised by Hung, Myers and Smolkin that the logarithmic term of entanglement entropy derived from Weyl anomaly of CFTs does not match the holographic result even if the extrinsic curvature vanishes. We find that such mismatch comes from the 'anomaly of entropy' of the derivative of curvature. After considering such contributions carefully, we resolve the puzzle successfully. In general, we need to fix the splitting problem for the conical metrics in order to derive the holographic entanglement entropy. We find that, at least for Einstein gravity, the splitting problem can be fixed by using equations of motion. How to derive the splittings for higher derivative gravity is a non-trivial and open question. For simplicity, we ignore the splitting problem in this paper and find that it does not affect our main results.

“…In order to compare this against the shear sum rule computed from field theory, we compute the parameters t 2 and t 4 for possible dual field theories at large N c but finite 't Hooft coupling λ c . Instead of directly computing the three point function of stress tensor from gravity, we compute the same from the conformal collider physics formalism of [15,[17][18][19].…”

Section: Jhep12(2017)156mentioning

confidence: 99%

Shear sum rule in higher derivative gravity theories

Chowdhury

2017

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.