On Holographic R\'enyi Entropy in Some Modified Theories of Gravity

TL;DR

This paper investigates holographic R\'enyi entropy in various modified gravity theories with 4D CFT duals, constructing solutions and verifying results through AdS/CFT correspondence, revealing bounds and consistency conditions.

Contribution

It introduces new perturbative solutions in Einsteinian cubic gravity and other modified theories, analyzing holographic R\'enyi entropy and dual CFT parameters.

Findings

Constructed perturbative black hole solutions in Einsteinian cubic gravity.

Computed R\'enyi entropy and twist operator dimensions in dual CFTs.

Identified bounds on parameters in quasi-topological gravity.

Abstract

We perform a detailed analysis of holographic entanglement R\'enyi entropy in some modified theories of gravity with four dimensional conformal field theory duals. First, we construct perturbative black hole solutions in a recently proposed model of Einsteinian cubic gravity in five dimensions, and compute the R\'enyi entropy as well as the scaling dimension of the twist operators in the dual field theory. Consistency of these results are verified from the AdS/CFT correspondence, via a corresponding computation of the Weyl anomaly on the gravity side. Similar analyses are then carried out for three other examples of modified gravity in five dimensions that include a chemical potential, namely Born-Infeld gravity, charged quasi-topological gravity and a class of Weyl corrected gravity theories with a gauge field, with the last example being treated perturbatively. Some interesting bounds in the dual conformal field theory parameters in quasi-topological gravity are pointed out. We also provide arguments on the validity of our perturbative analysis, whenever applicable.