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

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.

Schwinger pair production: Explicit Localization of the world-line instanton

“…The result yields the known Schwinger formula (1). In a similar vein, it is possible to show that the imaginary part of the sigma model functional integral for oriented open strings in a constant electric field is given exactly by the WKB limit of the semi-classical expansion about world-sheet instantons, and summing over instanton number [6].…”

Holographic Description of Noncommutative Schwinger Effect

“…Such methods were first introduced in [14]; the following closely follows [15,16]. For more sophisticated treatment, refer to [17,18]. The bosonic part of N = 4 SYM for the SU ðN + 1Þ theory in Euclidean signature reads as…”