Potential Analysis in Holographic Schwinger Effect

TL;DR

This paper investigates the electrostatic potential in the holographic Schwinger effect, reconciling different methods of calculating the Coulomb potential and confirming the critical electric field aligns with the Dirac-Born-Infeld (DBI) action, supporting the holographic model.

Contribution

The study reexamines Coulomb potential evaluation in holographic Schwinger effect, achieving complete agreement with DBI results and strengthening the holographic scenario.

Findings

Critical electric field deviates by 30% when using minimal surface calculation.

Reevaluating Coulomb potential via classical string action yields perfect agreement with DBI results.

Finite-temperature critical field also matches the DBI prediction.

Abstract

We analyze electrostatic potentials in the holographic Schwinger effect. The potential barrier for the pair production is estimated by a static potential consisting of static mass energies, an electric potential from an external electric-field, and the Coulomb potential between a particle and an antiparticle. Given that the Coulomb potential is supposed to be evaluated by the minimal surface attaching on the conformal boundary as usual, the critical field, where the potential barrier vanishes, exhibits a deviation of 30% from the one obtained from the Dirac-Born-Infeld (DBI) action. We reconsider this issue by reexamining the Coulomb-potential part, which is evaluated by the classical action of a string solution attaching on a probe D3-brane sitting at an intermediate position in the bulk AdS. Then the resulting critical-field completely agrees with the DBI result. This agreement gives rise to a strong support for the holographic scenario. We also discuss the finite-temperature case and the temperature-dependent critical-field also agrees with the DBI result.