Pseudo entropy and pseudo-Hermiticity in quantum field theories

TL;DR

This paper investigates pseudo Rènyi entropy in quantum field theories, revealing conditions for its reality, connecting it to pseudo-Hermiticity, and identifying universal divergent terms in 2D conformal field theories.

Contribution

It introduces the concept of pseudo Rènyi entropy in QFTs, links its properties to pseudo-Hermiticity, and uncovers universal divergence behavior in 2D CFTs.

Findings

Logarithmic term of pseudo Rènyi entropy is real when operators are in different Rindler wedges.

Connection established between pseudo Rènyi entropy properties and pseudo-Hermitian conditions.

Universal divergent term in 2D CFTs depends only on the operator's conformal dimension.

Abstract

In this paper, we explore the concept of pseudo R\'enyi entropy within the context of quantum field theories (QFTs). The transition matrix is constructed by applying operators situated in different regions to the vacuum state. Specifically, when the operators are positioned in the left and right Rindler wedges respectively, we discover that the logarithmic term of the pseudo R\'enyi entropy is necessarily real. In other cases, the result might be complex. We provide direct evaluations of specific examples within 2-dimensional conformal field theories (CFTs). Furthermore, we establish a connection between these findings and the pseudo-Hermitian condition. Our analysis reveals that the reality or complexity of the logarithmic term of pseudo R\'enyi entropy can be explained through this pseudo-Hermitian framework. Additionally, we investigate the divergent term of the pseudo R\'enyi entropy. Interestingly, we observe a universal divergent term in the second pseudo R\'enyi entropy within 2-dimensional CFTs. This universal term is solely dependent on the conformal dimension of the operator under consideration. For $n$-th pseudo R\'enyi entropy ($n\ge 3$), the divergent term is intricately related to the specific details of the underlying theory.