Renormalization of Supersymmetric Gauge Theories on Orbifolds: Brane Gauge Couplings and Higher Derivative Operators

TL;DR

This paper analyzes how supersymmetric gauge theories on orbifolds experience gauge coupling renormalization, revealing that hyper multiplets do not affect brane couplings on S^1/Z_2, but gauge couplings generally renormalize at fixed points in other orbifolds, requiring higher derivative operators.

Contribution

It provides a detailed one-loop renormalization analysis of gauge couplings in supersymmetric theories on various orbifolds, including the role of higher derivative operators.

Findings

Hyper multiplets do not renormalize brane gauge couplings on S^1/Z_2.

Gauge couplings renormalize at fixed points of T^2/Z_N orbifolds, except Z_2 fixed points.

Higher derivative operators are necessary to cancel divergences.

Abstract

We consider supersymmetric gauge theories coupled to hyper multiplets on five and six dimensional orbifolds and determine the bulk and local fixed point renormalizations of the gauge couplings. We infer from a component analysis that the hyper multiplet does not induce renormalization of the brane gauge couplings on the five dimensional orbifold S^1/Z_2. This is not due to supersymmetry, since the bosonic and fermionic contributions cancel separately. We extend this investigation to T^2/Z_N orbifolds using supergraph techniques in six dimensions. On general Z_N orbifolds the gauge couplings do renormalize at the fixed points, except for the Z_2 fixed points of an even ordered orbifold. To cancel the bulk one-loop divergences a dimension six higher derivative operator is needed, in addition to the standard bulk gauge kinetic term.