Replica trick and string winding

TL;DR

This paper uses the replica trick to compute string theory entropy, focusing on non-perturbative winding modes and tadpole cancellation, providing a target space interpretation in open and closed strings.

Contribution

It introduces a novel application of the replica trick to string theory entropy, emphasizing non-perturbative effects and tadpole conditions for correct moduli integration.

Findings

Derived a string entropy formula incorporating winding modes.

Provided a target space interpretation of the entropy in open and closed strings.

Highlighted the importance of tadpole cancellation in entropy calculations.

Abstract

We apply the replica trick to compute the entropy of a cylinder amplitude in string theory. We focus on the contribution from non-perturbative winding modes and impose tadpole cancellation to understand the correct prescription for integrating over moduli. Choosing the entangling surface to cut longitudinally over the whole length of the cylinder, we obtain an answer that is interpreted as the entropy of a density matrix. We recast this result in target space language, both in the open and closed string picture.