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 nR Riemann tensors (combined with n−nR Ricci’s) give rise to terms with up to 2nR− 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.
Highlights
In effectivegravity actions, higher-curvature terms appear as stringy and/or quantum corrections to the corresponding two-derivative actions — see e.g., [1,2,3]
The entanglement entropy (EE) for a region A in the boundary CFT is obtained as the area of the bulk surface, ΓA, which has the smallest area amongst all bulk surfaces which are homologous to A, divided by 4G, i.e., SHEEE(A)
We have found that the anomaly term in the holographic entanglement entropy functional can be written as 1 α 1 + qα
Summary
In effective (super)gravity actions, higher-curvature terms appear as stringy and/or quantum corrections to the corresponding two-derivative actions — see e.g., [1,2,3]. For the latter, we show that the functional dependence on the opening angle of the corner gets modified by the introduction of cubic densities with respect to the Einstein gravity result.
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