Schwinger pair production in AdS2

TL;DR

This paper investigates how charged particle pairs are produced in two-dimensional Anti-de Sitter space under a constant electric field, revealing a threshold condition for pair production influenced by the AdS geometry.

Contribution

It provides a detailed analysis of Schwinger pair production in AdS_2, including both semi-classical and quantum calculations, and identifies a critical electric field threshold for vacuum instability.

Findings

Pair production requires E^2 > M^2 + 1/4 in AdS_2.

Electric field raises the Breitenlohner-Freedman bound.

Results aid in constructing supersymmetric AdS_2 x S^2 string vacua.

Abstract

We analyze the pair production of charged particles in two-dimensional Anti-de Sitter space (AdS_2) with a constant, uniform electric field. We compute the production rate both at a semi-classical level, viewing Schwinger pair production as a tunneling event, and at the full quantum level, by extracting the imaginary part of the one-loop amplitude. In contrast to the usual Schwinger pair production in flat space, pair production in AdS_2 requires a sufficiently large electric field E^2> M^2+1/4 in order to overcome the confining effect of the AdS geometry -- put in another way, the presence of an electric field E raises the Breitenlohner-Freedman bound to M^2 > -1/4 + E^2. For E greater than this threshold, the vacuum is unstable to production of charged pairs in the bulk. We expect our results to be helpful in constructing supersymmetric AdS_2 X S^2 perturbative string vacua, which enter in the near-horizon limit of extremal charged black holes. Although the generalized Breitenlohner-Freedman bound is obeyed in these cases, production of BPS particles at threshold is possible and relevant for AdS_2 fragmentation.