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Schwinger pair production in AdS2

B. Pioline, J. Troost

TL;DR

This work analyzes Schwinger pair production of charged particles in AdS_2 under a constant electric field, revealing a threshold $E^2 > M^2 + 1/4$ set by AdS confinement and a generalized BF bound $M^2 > -1/4 + E^2$. The authors develop both a semiclassical tunneling picture and a full quantum one-loop calculation, using analytic continuation from the Landau problem on $H_2$ to AdS_2 and a mini-superspace approach; they derive explicit imaginary parts of the vacuum amplitude for scalar and spinor fields, expressed in terms of polylogarithms, and recover flat-space behavior at large $E$. The results connect to near-horizon AdS_2 x S^2 vacua, potentially informing black hole microphysics, AdS fragmentation, and string theory in AdS_2 backgrounds, while highlighting the dependence on vacuum/boundary conditions and possible gravitational corrections. The work provides a concrete framework to study electromagnetic phenomena in strongly curved spacetimes and suggests extensions to global AdS_2, higher spins, and brane configurations in AdS/CFT contexts.

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.

Schwinger pair production in AdS2

TL;DR

This work analyzes Schwinger pair production of charged particles in AdS_2 under a constant electric field, revealing a threshold set by AdS confinement and a generalized BF bound . The authors develop both a semiclassical tunneling picture and a full quantum one-loop calculation, using analytic continuation from the Landau problem on to AdS_2 and a mini-superspace approach; they derive explicit imaginary parts of the vacuum amplitude for scalar and spinor fields, expressed in terms of polylogarithms, and recover flat-space behavior at large . The results connect to near-horizon AdS_2 x S^2 vacua, potentially informing black hole microphysics, AdS fragmentation, and string theory in AdS_2 backgrounds, while highlighting the dependence on vacuum/boundary conditions and possible gravitational corrections. The work provides a concrete framework to study electromagnetic phenomena in strongly curved spacetimes and suggests extensions to global AdS_2, higher spins, and brane configurations in AdS/CFT contexts.

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.

Paper Structure

This paper contains 13 sections, 82 equations.

Table of Contents

  1. Introduction
  2. Semi-classics of a charged particle in $AdS_2$
  3. Classical trajectories of a charged particle in $AdS_2$
  4. Spectrum generating $Sl(2,\mathbb{R})$ symmetry
  5. Tunneling and semi-classical Schwinger pair production
  6. Periodic trajectories and mini-superspace path integral
  7. One-loop vacuum amplitude in quantum field theory
  8. One-loop amplitude on $H_2$
  9. Analytic continuation to $AdS_2$
  10. Spin 1/2 case
  11. Summary and Discussion
  12. Zeta function regularisation
  13. Gravitational back-reaction