On Schwinger Pair Creation in Gravity and in Closed Superstring Theory

TL;DR

This paper derives a comprehensive formula for Schwinger pair creation in gravitational backgrounds within superstring theory, revealing novel dependencies on electric field strength and the influence of gravitational effects.

Contribution

It provides the first closed-form expression for pair creation rate including gravitational back reaction in superstring models, connecting field theory and string theory results.

Findings

Pair creation rate matches Schwinger formula at weak fields with Unruh effect contribution.

Rate becomes constant at strong electric fields in four dimensions.

Kaluza-Klein states exhibit power-law dependence, not exponential, on electric field.

Abstract

We investigate the Schwinger pair creation process in the context of gravitational models with the back reaction of the electric field included in the geometry. The background is also an exact solution of type II superstring theory, where the electric field arises by Kaluza-Klein reduction. We obtain a closed formula for the pair creation rate that incorporates the gravitational back reaction. At weak fields it has the same structure as the general Schwinger formula, albeit pairs are produced by a combination of Schwinger and Unruh effect, the latter due to the presence of a Rindler horizon. In four spacetime dimensions, the rate becomes constant at strong electric fields. For states with mass of Kaluza-Klein origin, the rate has a power-like dependence in the electric field, rather than the familiar (non-perturbative) exponential dependence. We also reproduce the same formula from the string partition function for winding string states. Finally, we comment on the generalization to excited string states.