Roles of electric field/time-dependent Wilson line in toroidal compactification with or without magnetic fluxes

TL;DR

This paper explores how electric fields along compact dimensions influence gauge theories with or without magnetic fluxes, revealing effects like KK particle production and flavor structure modifications relevant to early universe physics.

Contribution

It analyzes the impact of time-dependent Wilson lines and electric fields on Kaluza-Klein modes in toroidal compactifications with magnetic fluxes, highlighting different physical effects.

Findings

Without magnetic flux, KK particle production occurs via the Schwinger effect.

With magnetic flux, KK production is suppressed but flavor structures are affected.

Electric fields influence the KK spectrum and low-energy effective theories.

Abstract

We discuss the effects of electric fields along compact directions within (supersymmetric) gauge theory in $\mathbb{R}^{1,3}\times{\mathbb T}^2 (\times{\mathbb T}^2\times{\mathbb T}^2)$. The electric field along compact directions is equivalent to time-dependent homogeneous configuration of Wilson line moduli, which would be relevant to physics in the early universe. In particular, we consider models with and without background magnetic fluxes, which lead to completely different effects of the electric field due to the difference in the Kaluza-Klein (KK) level structure. We show that, in the case without magnetic fluxes, the deceleration of KK momenta may cause non-perturbative KK particle production dubbed as the KK Schwinger effect, whereas in the case with magnetic flux such KK particle production does not take place but flavor structure of low energy effective theory may be affected.