Holographic Description of Noncommutative Schwinger Effect

Udit Narayan Chowdhury

doi:10.1155/2021/6648322

Abstract

We consider the phenomenon of spontaneous pair production in the presence of an external electric field for noncommutative Yang-Mills theories. Using Maldacena’s holographic conjecture, the threshold electric field for pair production is computed from the quark/antiquark potential for noncommutative theories. As an effect of noncommutativity, the threshold electric field is seen to be smaller than its commutative counterpart. We also estimate the correction to the production rate of quark/antiquark pairs to the first order of the noncommutative deformation parameter. Our result bears resemblance with an earlier related work (based on field-theoretic methods).

Highlights

Quantum field theory is primarily studied in its perturbative regime
The exponential suppression hints that the pair production process can be modeled as quantum mechanical tunneling in a certain potential barrier
If the external electric field is less than the confining string tension σstr, the pair production is prohibited as the effective potential barrier remains positive instead of dumping out at large qq separation

Summary

Introduction

Quantum field theory is primarily studied in its perturbative regime. there exist quite some novel nonperturbative features of quantum field theories amongst which the Schwinger effect [1] stands its ground (for a recent review, see [2]). If the virtual pairs are separated by a distance x∗ such that 1/2eEx∗ = m the electron (and the positron) becomes a real particle as it has the required rest mass energy This value x∗ = 2m/eE is the width of the potential barrier. I.e., E < m2/eα, there exist two zero points of the potential profile and the potential is positive in intermediate regimes of separation x In this case, the particles become real by tunneling through this barrier and the production rate is exponentially suppressed as described by the Schwinger formula. If the external electric field is less than the confining string tension σstr, the pair production is prohibited as the effective potential barrier remains positive instead of dumping out at large qq separation.

Pair Production and Noncommutativity

Potential Analysis of the Noncommutative Schwinger Effect

1: L ð41Þ

Pair Production Rate of the Noncommutative Schwinger Effect

K coth s0

Conclusions