Worldsheet Instantons and the amplitude for string pair production in an external field as a WKB exact functional integral

TL;DR

This paper analyzes charged string pair creation in a constant electric field using worldsheet instantons, showing that the WKB approximation captures the exact amplitude due to a fermionic symmetry that localizes the functional integral.

Contribution

It demonstrates that the string pair production amplitude can be exactly obtained via a WKB approximation by identifying a fermionic symmetry that ensures localization.

Findings

WKB approximation reproduces the exact amplitude

Fermionic symmetry leads to localization of the functional integral

Multi-instanton sum matches known pair production amplitude

Abstract

We revisit the problem of charged string pair creation in a constant external electric field. The string states are massive and creation of pairs from the vacuum is a tunnelling process, analogous to the Schwinger process where charged particle-anti-particle pairs are created by an electric field. We find the instantons in the worldsheet sigma model which are responsible for the tunnelling events. We evaluate the sigma model partition function in the multi-instanton sector in the WKB approximation which keeps the classical action and integrates the quadratic fluctuations about the solution. We find that the summation of the result over all multi-instanton sectors reproduces the known amplitude. This suggests that corrections to the WKB limit must cancel. To show that they indeed cancel, we identify a fermionic symmetry of the sigma model which occurs in the instanton sectors and which is associated with collective coordinates. We demonstrate that the action is symmetric and that the interaction action is an exact form. These conditions are sufficient for localization of the worldsheet functional integral onto its WKB limit.