# Wilson lines and UV sensitivity in magnetic compactifications

## TL;DR

This paper analyzes the UV behavior of 6D supersymmetric gauge theories compactified on a torus with magnetic flux, computing one-loop corrections to understand divergences and counterterms in the effective theory.

## Contribution

It introduces a detailed offshell calculation of Wilson line self-energy corrections in magnetic flux compactifications, identifying a new higher-dimensional counterterm.

## Key findings

- Discovery of a new dimension-6 counterterm enhanced by compactification area
- Identification of UV divergences requiring specific counterterms
- Comparison with fluxless orbifold compactifications

## Abstract

We investigate the ultraviolet (UV) behaviour of 6D N=1 supersymmetric effective (Abelian) gauge theories compactified on a two-torus ($T_2$) with magnetic flux. To this purpose we compute offshell the one-loop correction to the Wilson line state self-energy. The offshell calculation is actually necessary to capture the usual effective field theory expansion in powers of $(\partial/\Lambda)$. Particular care is paid to the regularization of the (divergent) momentum integrals, which is relevant for identifying the corresponding counterterm(s). We find a counterterm which is a new higher dimensional effective operator of dimension d=6, that is enhanced for a larger compactification area (where the effective theory applies) and is consistent with the symmetries of the theory. Its consequences are briefly discussed and comparison is made with orbifold compactifications without flux.