LREE of an Unstable Dressed-Dynamical D$p$-brane: Superstring Calculations

TL;DR

This paper calculates the left-right entanglement entropy (LREE) for a Dp-brane with motion and background fields in superstring theory, analyzing its behavior during tachyon condensation and implications for brane stability.

Contribution

It introduces a method to compute LREE for unstable Dp-branes with background fields and explores its evolution during tachyon condensation in superstring frameworks.

Findings

LREE decreases during tachyon condensation indicating brane collapse

Derived constraints consistent with the second law of thermodynamics

Established a link between entanglement entropy and brane stability

Abstract

We obtain the left-right entanglement entropy (LREE) for a D$p$-brane with tangential motion in the presence of a $U(1)$ gauge potential, the Kalb-Ramond field and an open string tachyon field. Thus, at first we extract the R\'{e}nyi entropy and then by taking a special limit of it we acquire the entanglement entropy. We shall investigate the behavior of the LREE under the tachyon condensation phenomenon. We observe that the deformation of the LREE, through this process, reveals the collapse of the brane. Besides, we examine the second law of thermodynamics for the LREE under tachyon condensation, and we extract the imposed constraints. Note that our calculations will be in the context of the type IIA/IIB superstring theories.