The disk partition function in string theory

We investigate the disk partition function for the open string. This is a subtle problem because of the presence of a residual gauge group PSL(2, R) on the worldsheet even after fixing the conformal gauge. It naively has infinite volume and leads to a vanishing answer. We use different methods that all demonstrate that PSL(2, R) effectively behaves like a group with finite negative volume in the path integral, which leads to a simple prescription for the computation of the disk partition function. We apply our findings to give a simple rederivation of the D-brane tensions.

Automated summary

This study focuses on the disk partition function of open strings, addressing the subtle issue arising from the residual gauge group PSL(2, R). Various methods demonstrate that PSL(2, R) effectively behaves like a group with finite negative volume in the path integral, leading to a simple prescription for computation. The findings are then applied to offer a straightforward rederivation of D-brane tensions.