Holographic entanglement entropy for perturbative higher-curvature gravities

TL;DR

This paper develops a simplified, perturbative approach to compute holographic entanglement entropy functionals for higher-curvature gravities, enabling explicit calculations and revealing new features in universal terms.

Contribution

It introduces a novel rewriting of the entanglement entropy functional that simplifies calculations for cubic and quartic theories, including Lovelock gravities.

Findings

Explicit formulas for higher-curvature entanglement functionals

Demonstration of the anomaly term structure in Lovelock theories

Modification of corner region universal terms in $d=3$

Abstract

The holographic entanglement entropy functional for higher-curvature gravities involves a weighted sum whose evaluation, beyond quadratic order, requires a complicated theory-dependent splitting of the Riemann tensor components. Using the splittings of general relativity one can obtain unambiguous formulas perturbatively valid for general higher-curvature gravities. Within this setup, we perform a novel rewriting of the functional which gets rid of the weighted sum. The formula is particularly neat for general cubic and quartic theories, and we use it to explicitly evaluate the corresponding functionals. In the case of Lovelock theories, we find that the anomaly term can be written in terms of the exponential of a differential operator. We also show that order-$n$ densities involving $n_R$ Riemann tensors (combined with $n-n_R$ Ricci's) give rise to terms with up to $2n_R-2$ extrinsic curvatures. In particular, densities built from arbitrary Ricci curvatures combined with zero or one Riemann tensors have no anomaly term in their functionals. Finally, we apply our results for cubic gravities to the evaluation of universal terms coming from various symmetric regions in general dimensions. In particular, we show that the universal function characteristic of corner regions in $d=3$ gets modified in its functional dependence on the opening angle with respect to the Einstein gravity result.