Wilson-line Scalar as a Nambu-Goldstone Boson in Flux Compactifications and Higher-loop Corrections

TL;DR

This paper investigates a scalar zero mode in a six-dimensional flux compactification, confirming it as a Nambu-Goldstone boson and analyzing its masslessness up to two-loop order and beyond.

Contribution

It explicitly demonstrates the scalar zero mode as a Nambu-Goldstone boson and examines its mass stability under higher-loop corrections in flux compactifications.

Findings

Scalar zero mode is a Nambu-Goldstone boson due to flux-induced symmetry breaking.

The mode remains massless up to two-loop corrections.

Higher-order contributions to the effective potential are discussed.

Abstract

We study a scalar zero mode originated from extradimensional components of a gauge field in a six-dimensional theory compactified on a magnetized torus. We confirm it is a Nambu-Goldstone boson of the translational symmetry on the torus which is breaking spontaneously due to magnetic flux. We also show explicitly it is massless up to the two-loop level. Moreover, we discuss full order contributions by considering the effective potential.