Entanglement Entropy for Open Bosonic Strings on $Dp$-branes

TL;DR

This paper calculates the entanglement entropy of open bosonic strings on Dp-branes using covariant string field theory, revealing area-law behavior and divergences mainly due to tachyons, with finiteness in certain dimensions.

Contribution

It provides a covariant string field theory computation of entanglement entropy for open strings on Dp-branes, highlighting divergence structures and the role of tachyons.

Findings

Entanglement entropy is proportional to the boundary area of the bipartition.

Divergences are mainly due to tachyon contributions, absent in supersymmetric theories.

Entanglement entropy is finite for 2 ≤ p ≤ d_critical - 2 and logarithmically divergent for p=1 and p=d_critical-1.

Abstract

We study the entanglement entropy for open bosonic strings on multiple $Dp$-branes by using the covariant open string field theory. Choosing one of the spatial coordinates which are tangential to the hyperplane on which $Dp$-branes are located, we divide the hyperplane into two halves. By using the string wavefunction in the Fock space representation, we evaluate the entanglement entropy. The entanglement entropy is found to be proportional to the area of $(p-1)$-dimensional boundary of the bipartite hyperplanes and divergent in the ultraviolet (UV) region as well as in the infrared (IR) region. However, the leading divergences are mainly due to tachyon contributions to the entanglement entropy, which may be absent in supersymmetric string theories. Apart from the divergences thanks to tachyons, the entanglement entropy for open bosonic strings on $Dp$-branes is finite for $2 \le p \le d_{\text{critical}} -2$ and logarithmically divergent for $p =1, d_{\text{critical}}-1$.