Pseudo entropy and pseudo-Hermiticity in quantum field theories

A bstract In this paper, we explore the concept of pseudo Rényi 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 Rényi 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 Rényi entropy can be explained through this pseudo-Hermitian framework. Additionally, we investigate the divergent term of the pseudo Rényi entropy. Interestingly, we observe a universal divergent term in the second pseudo Rényi entropy within 2-dimensional CFTs. This universal term is solely dependent on the conformal dimension of the operator under consideration. For n -th pseudo Rényi entropy ( n ≥ 3), the divergent term is intricately related to the specific details of the underlying theory.