# Cancellation of One-loop Corrections to Scalar Masses in Yang-Mills Theory with Flux Compactification

## TL;DR

This paper demonstrates that one-loop quantum corrections to scalar masses in a six-dimensional Yang-Mills theory with flux compactification are exactly canceled due to a shift symmetry, confirming the Nambu-Goldstone nature of the zero mode.

## Contribution

It shows the exact cancellation of one-loop scalar mass corrections in flux compactified Yang-Mills theory due to translational shift symmetry.

## Key findings

- One-loop corrections to scalar masses are canceled.
- Zero mode acts as a Nambu-Goldstone boson.
- Shift symmetry ensures mass protection.

## Abstract

We calculate one-loop corrections to the mass for the zero mode of scalar field in a six-dimensional Yang-Mills theory compactified on a torus with magnetic flux. It is shown that these corrections are exactly cancelled thanks to a shift symmetry under the translation in extra spaces. This result is expected from the fact that the zero mode of scalar field is a Nambu-Goldstone boson of the translational invariance in extra spaces.