Relative entropy of excited states in conformal field theories of arbitrary dimensions

TL;DR

This paper computes the leading relative entropy between reduced density matrices of globally excited states in conformal field theories across arbitrary dimensions, using the replica trick and the CHM map to reduce the problem to correlation functions on $S^1\times H^{d-1}$. It derives explicit leading-order results for scalar, stress-tensor, and current exchanges in the small-subsystem limit, and confirms these by holographic calculations via the Ryu-Takayanagi prescription in AdS/CFT. The work also analyzes the first asymmetric corrections beyond leading order, provides a 2d check, and connects the average relative entropy over an energy window to the variance of OPE coefficients, with implications for black hole microstate distinguishability in holography and for large-$N$ theories. Overall, the results establish a dimensionally robust framework linking CFT OPE data to relative entropy and holographic entanglement, highlighting universal aspects of entanglement and information measures in strongly coupled quantum systems.

Abstract

Extending our previous work, we study the relative entropy between the reduced density matrices obtained from globally excited states in conformal field theories of arbitrary dimensions. We find a general formula in the small subsystem size limit. When one of the states is the vacuum of the CFT, our result matches with the holographic entanglement entropy computations in the corresponding bulk geometries, including AdS black branes. We also discuss the first asymmetric part of the relative entropy and comment on some implications of the results on the distinguishability of black hole microstates in AdS/CFT.