Schwinger Pair Production in Hot Anti-de Sitter Space

TL;DR

This paper analyzes particle production in thermal Anti-de Sitter space under a constant electric field, revealing that finite temperature enhances the Schwinger pair production rate and identifying a critical temperature affecting this process.

Contribution

It introduces a semi-classical method to compute Schwinger pair production in AdS space at finite temperature, highlighting the thermal enhancement and a critical temperature effect.

Findings

Particle production rate increases with temperature.

Existence of a critical temperature influencing pair production.

Application of WKB approximation to AdS space.

Abstract

We consider particle production in $1+1$ dimensional thermal Anti-de Sitter space under the influence of a constant electric field. The vacuum-persistence amplitude is given by a non-relativistic tunnelling instanton once we interpret the system as being governed by an "equivalent" non-relativistic Schr\"odinger equation. Working in the WKB approximation, we calculate the tunnelling rate in anti de Sitter space at finite temperature and observe that the particle production rate is enhanced. Additionally, it is observed that there is a critical temperature beyond which the production rate is affected by the thermal environment. We claim this to be a new result for Anti-de Sitter space in the semi-classical approximation.