Schwinger pair production in AdS 2

We analyze the pair production of charged particles in two-dimensional Antide Sitter space (AdS2) 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 AdS2 requires a sufficiently large electric field E2 > M2+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 M2 > −1/4+E2. 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 AdS2 × S2 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 AdS2 fragmentation.