Renyi reflected entropy and entanglement wedge cross section with cosmic branes in AdS/BCFT

TL;DR

This paper explores the relationship between Renyi reflected entropy and entanglement wedge cross section with cosmic branes in AdS/BCFT, revealing a duality and phase richness in holographic entanglement measures.

Contribution

It establishes a duality between cosmic brane backreaction effects and Renyi reflected entropy in AdS/BCFT, extending understanding of entanglement wedge cross sections in holography.

Findings

Derived the $m-1$ correction to reflected entropy in AdS/BCFT.

Showed the duality between entanglement wedge cross section with cosmic branes and Renyi reflected entropy.

Provided insights for an $oldsymbol{ ext{ extit{epsilon}}}$-expansion of five-point functions in holographic CFTs.

Abstract

In this study, we calculate the $m-1$ correction to the reflected entropy for two adjacent intervals on a half-infinite line within the AdS$_3$/BCFT$_2$ framework, where $m$ is a Renyi index for a canonical purification. We utilize the doubling trick and compute the leading terms in the large central charge expansion of correlation functions in the holographic BCFT. In the corresponding AdS space with an end of the world brane, we analyze the entanglement wedge cross section, the dual counterpart of reflected entropy. This AdS/BCFT setup allows us to explore a richer set of phases in the entanglement wedge cross section. The $m-1$ correction in the holographic BCFT manifests as modifications in the entanglement wedge cross section induced by cosmic branes. For the adjacent intervals anchored to the boundary of BCFT, we show the duality between the entanglement wedge cross section with the backreaction from a cosmic brane and Renyi reflected entropy at all orders in $m-1$. Furthermore, by analyzing the entanglement wedge cross section for general adjacent intervals, we provide guidance for an $\epsilon$-expansion of five-point functions in the holographic CFT, where $\epsilon$ is the rescaled conformal dimension by the central charge.