One-loop effective potential in M4 x T2 with and without 't Hooft flux

TL;DR

This paper reviews compactification with background flux, focusing on one-loop effective potentials in six-dimensional models with trivial and non-trivial 't Hooft flux, highlighting flux effects on symmetry breaking and chiral fermion generation.

Contribution

It provides the first calculation of one-loop effective potential in non-trivial 't Hooft flux scenarios in six-dimensional models, extending previous trivial flux results.

Findings

Reproduces known results for trivial 't Hooft flux case.

Calculates new one-loop contributions for non-trivial 't Hooft flux.

Shows flux influences symmetry breaking and fermion chirality.

Abstract

We review the basic notions of compactification in the presence of a background flux. In extra-dimentional models with more than five dimensions, Scherk and Schwarz boundary conditions have to satisfy 't Hooft consistency conditions. Different vacuum configurations can be obtained, depending whether trivial or non-trivial 't Hooft flux is considered. The presence of the "magnetic" background flux provide, in addition, a mechanism for producing four-dimensional chiral fermions. Particularizing to the six-dimensional case, we calculate the one-loop effective potential for a U(N) gauge theory on M4 x T2. We firstly review the well known results of the trivial 't Hooft flux case, where one-loop contributions produce the usual Hosotani dynamical symmetry breaking. Finally we applied our result for describing, for the first time, the one-loop contributions in the non-trivial 't Hooft flux case.