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

TL;DR

This paper derives a general formula for the relative entropy between excited and vacuum states in conformal field theories across dimensions, linking it to holographic entanglement entropy and black hole microstate distinguishability.

Contribution

It provides a universal formula for relative entropy in arbitrary-dimensional CFTs and connects it to holographic computations and black hole microstate analysis.

Findings

Matching with holographic entanglement entropy in AdS geometries

Derived a general formula in the small subsystem limit

Discussed implications for black hole microstate distinguishability

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.