Left-Right Entanglement Entropy of Dp-branes

TL;DR

This paper calculates the left-right entanglement entropy for Dp-branes in string theory using a conformal field theory approach, exploring ambiguities, T-duality effects, and its relation to boundary entropy and brane tension.

Contribution

It introduces a method to compute Dp-brane entanglement entropy via CFT, analyzing ambiguities and T-duality, and relates it to boundary entropy and brane tension.

Findings

Entanglement entropy computed as von Neumann entropy of a density matrix.

T-duality acts covariantly on the entanglement entropy.

Left-right entanglement entropy generalizes boundary entropy and D-brane tension.

Abstract

We compute the left-right entanglement entropy for Dp-branes in string theory. We employ the CFT approach to string theory Dp-branes, in particular, its presentation as coherent states of the closed string sector. The entanglement entropy is computed as the von Neumann entropy for a density matrix resulting from integration over the left-moving degrees of freedom. We discuss various crucial ambiguities related to sums over spin structures and argue that different choices capture different physics; however, we advance a themodynamic argument that seems to favor a particular choice of replica. We also consider Dp branes on compact dimensions and verify that the effects of T-duality act covariantly on the Dp brane entanglement entropy. We find that generically the left-right entanglement entropy provides a suitable generalization of boundary entropy and of the D-brane tension.