Generalized entanglement entropies in two-dimensional conformal field theory

TL;DR

This paper introduces generalized Rényei entropies in 2D conformal field theories, linking them to four-point correlators and providing computational methods for free bosonic models, enhancing understanding of entanglement in CFTs.

Contribution

It defines and analyzes generalized Rényei entropies in 2D CFTs, establishing their relation to correlators and developing efficient computation strategies for free bosonic theories.

Findings

Generalized Rényei entropies reduce to standard ones when indices match.

Second generalized Rényei entropies are expressed as four-point correlators.

New results for Rényei and relative entropies involving descendant states.

Abstract

We introduce and study generalized R\'enyi entropies defined through the traces of products of ${\rm Tr}_B (|\Psi_i\rangle\langle \Psi_j|)$ where $|\Psi_i\rangle$ are eigenstates of a two-dimensional conformal field theory (CFT). When $|\Psi_i\rangle=|\Psi_j\rangle$ these objects reduce to the standard R\'enyi entropies of the eigenstates of the CFT. Exploiting the path integral formalism, we show that the second generalized R\'enyi entropies are equivalent to four-point correlators. We then focus on a free bosonic theory for which the mode expansion of the fields allows us to develop an efficient strategy to compute the second generalized R\'enyi entropy for all eigenstates. As a byproduct, our approach also leads to new results for the standard R\'enyi and relative entropies involving arbitrary descendent states of the bosonic CFT.