CFT correlators from shape deformations in Cubic Curvature Gravity

TL;DR

This paper derives a covariant holographic entanglement entropy functional for higher curvature gravities, computes stress-tensor correlator coefficients in dual CFTs, and compares different splitting methods, confirming the non-minimal splitting approach.

Contribution

It introduces a covariant entanglement entropy functional for higher curvature gravities and clarifies the correct splitting method for computing stress-tensor correlators in holography.

Findings

The non-minimal splitting yields consistent $t_4$ coefficients.

The minimal splitting approach is inconsistent for $t_4$ calculation.

The derived functional applies to CFTs dual to cubic curvature gravity.

Abstract

We find a covariant expression for the universal part of the holographic entanglement entropy which is valid for CFTs dual to generic higher curvature gravities in up to five bulk dimensions. We use this functional to compute universal coefficients of stress-tensor correlators in three-dimensional CFTs dual to Cubic Curvature Gravity. Using gauge/gravity duality, we work out an expression for the entanglement entropy of deformed entangling regions and read the coefficients from the power expansion of the entropy in the deformation parameter. In particular, we obtain the $t_4$ coefficient of the 3-point function and exhibit a difference between the results obtained using the entanglement entropy functional for minimal and non-minimal splittings. We compare the obtained expressions for $t_{4}$ derived considering both splittings with results obtained through other holographic methods which are splitting-independent. We find agreement with the result obtained from the non-minimal splitting, whereas the result derived from the minimal splitting is inconsistent and it is therefore ruled out.