Stretched strings and worldsheets with a handle

TL;DR

This paper demonstrates that the stretched string interpretation remains valid for multiloop amplitudes in string theory with a background NS two-form field, connecting string theory computations with noncommutative field theory results.

Contribution

It constructs worldsheet partition functions and propagators for worldsheets with a handle and boundary, extending the stretched string picture to multiloop amplitudes.

Findings

Stretched string interpretation applies to two-loop nonplanar vacuum bubble amplitudes.

Worldsheet computations reduce to noncommutative field theory amplitudes in the decoupling limit.

The analysis confirms the validity of the stretched string picture in multiloop contexts.

Abstract

In the presence of the constant background NS two-form gauge field, we construct the worldsheet partition functions, bulk propagators and boundary propagators for the worldsheets with a handle and a boundary. We analyze the noncommutative $\phi^3$ field theory amplitudes that correspond to the general two-point insertions on the two-loop nonplanar vacuum bubble. By the direct string theory amplitude computations on the worldsheets with a handle, which reduce to the aforementioned field theory amplitudes in the decoupling limit, we find that the stretched string interpretation remains valid for the types of amplitudes in consideration. This completes the demonstration that the stretched string picture holds up in the general multiloop context.