Abstract
We perform a detailed analysis of holographic entanglement Rényi 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 Rényi 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.
Highlights
Ryu-Takayangi prescription and its generalisations [9,10,11,12,13,14] have been at the forefront of research over the last decade and promises to yield a deep understanding of entanglement in strongly coupled quantum systems
X1 dS T (x) dx xn dx where in the second line we have done an integration by parts. It follows that x1 and xn (the upper and lower limits, respectively, in eq (3.18)) are the only two remaining quantities that we need for the computation of the entanglement Renyi entropy (ERE)
We present the results for the ERE in Einsteinian cubic gravity (ECG), plotted against two quantities, namely the order of the ERE n and the coupling β
Summary
We will briefly review the relevant details of the computation of various quantities associated with holographic ERE. This proposal of ERE was generalized by [34] to include a chemical potential in the field theory They constructed the charged entanglement Renyi entropy in a grand canonical ensemble where one has to compute the Euclidean path integral by inserting a Wilson line encircling the entangling surface. As we have mentioned, the replica trick for computing the Renyi entropy can be understood as the insertion of a surface operator, known as the twist operator (σn), at the entangling surface [28, 34, 52]. Following [28, 34], we quote the final expression of the scaling dimension hn (in the four dimensional boundary CFT) in terms of the thermal energy density, n R3 hn(μc) = 3 T0 E(T0, 0) − E. Having set up the notations and conventions, we will proceed to the main body of this paper
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
