One-Loop Effective Action and Schwinger Effect in (Anti-) de Sitter Space

TL;DR

This paper analyzes the Schwinger effect in (Anti-) de Sitter spaces, deriving the exact one-loop effective action and pair-production rates, and interprets these results thermally via Gibbons-Hawking and Unruh temperatures.

Contribution

It provides the exact one-loop effective action and pair-production rates in (A)dS spaces, with a novel thermal interpretation linking curvature effects to temperature concepts.

Findings

Exact pair-production rates derived for (A)dS spaces.

Thermal interpretation of Schwinger effect in curved spacetime.

Pole structure analysis of the effective action.

Abstract

We study the Schwinger mechanism by a uniform electric field in ${\rm dS}_2$ and ${\rm AdS}_2$ and the curvature effect on the Schwinger effect, and further propose a thermal interpretation of the Schwinger formula in terms of the Gibbons-Hawking temperature and the Unruh temperature for an accelerating charge in ${\rm dS}_2$ and an analogous expression in ${\rm AdS}_2$. The exact one-loop effective action is found in the proper-time integral in each space, which is determined by the effective mass, the Maxwell scalar, and the scalar curvature, and whose pole structure gives the imaginary part of the effective action and the exact pair-production rate. The exact pair-production rate is also given the thermal interpretation.