Effective field theory for magnetic compactifications

TL;DR

This paper derives the complete four-dimensional effective action for supersymmetric gauge theories compactified on a fluxed torus, revealing how magnetic flux influences the mass spectrum, interactions, and quantum corrections, including the vanishing of one-loop corrections.

Contribution

It provides a comprehensive derivation of the effective action incorporating flux effects, including charged states, mass spectrum, and quantum corrections, which was not fully addressed before.

Findings

One-loop corrections to mass and couplings vanish with flux.

Magnetic flux induces spontaneous symmetry breaking and affects Wilson line dynamics.

The effective action includes a tower of charged states and their interactions.

Abstract

Magnetic flux plays an important role in compactifications of field and string theories in two ways, it generates a multiplicity of chiral fermion zero modes and it can break supersymmetry. We derive the complete four-dimensional effective action for N=1 supersymmetric Abelian and non-Abelian gauge theories in six dimensions compactified on a torus with flux. The effective action contains the tower of charged states and it accounts for the mass spectrum of bosonic and fermionic fields as well as their level-dependent interactions. This allows us to compute quantum corrections to the mass and couplings of Wilson lines. We find that the one-loop corrections vanish, contrary to the case without flux. This can be traced back to the spontaneous breaking of a symmetry of the six-dimensional theory by the background gauge field, with the Wilson line as Goldstone boson.