Partition Function on Not-flat Brane

TL;DR

This paper demonstrates that the partition function for a not-flat D1-brane can be expressed similarly to that of a flat brane at the first order in alpha-prime, with curvature effects encoded in the tachyon beta function.

Contribution

It introduces a method to represent the partition function of curved D1-branes in a form analogous to flat branes, incorporating curvature through the tachyon beta function.

Findings

Partition function on not-flat D1-brane matches flat case at alpha'-order

Curvature information is captured by the tachyon beta function

Provides a unified framework for flat and curved brane partition functions

Abstract

We show that a partition function on the not-flat D1-brane can be written in the same form as that on the flat one in $\alpha^\prime$-order. In this case the information of the curvature of the brane configuration is included in tachyon beta function.