Worldlines on Orbifolds and the Fayet-Iliopoulos Term

TL;DR

This paper develops a string-inspired worldline approach to compute one-loop effects on orbifolds, including brane interactions and supersymmetry breaking, exemplified by the Fayet-Iliopoulos term.

Contribution

It introduces a novel worldline technique for orbifold calculations that incorporates brane-localized terms and supersymmetry breaking effects.

Findings

Reproduces known Fayet-Iliopoulos term results

Generalizes to include brane-localized soft SUSY breaking masses

Provides a flexible method for one-loop orbifold computations

Abstract

We adapt ``string-inspired'' worldline techniques to one-loop calculations on orbifolds, in particular on the $S^1/Z_2$ orbifold. Our method also allows for the treatment of brane-localized terms, or bulk-brane couplings. For demonstration, we reproduce the well-known result for the one-loop induced Fayet-Iliopoulos term in rigidly supersymmetric Abelian gauge theory, and generalize it to the case where soft supersymmetry breaking mass terms for the bulk scalar fields are present on the branes.