Quantum Corrections to Non-Abelian SUSY Theories on Orbifolds

TL;DR

This paper investigates quantum corrections in supersymmetric non-Abelian gauge theories on orbifolds, revealing how gauge couplings and higher derivative operators are renormalized at fixed points to maintain gauge invariance.

Contribution

It extends supergraph techniques to orbifolds and analyzes the renormalization of gauge couplings and operators in 5D and 6D SUSY theories on orbifolds.

Findings

Bulk gauge kinetic terms are required to cancel one-loop divergences.

Gauge couplings renormalize at fixed points due to vector multiplet interactions.

Higher derivative operators and Wess-Zumino-Witten terms are necessary for gauge invariance.

Abstract

We consider supersymmetric non-Abelian gauge theories coupled to hyper multiplets on five and six dimensional orbifolds, S^1/Z_2 and T^2/Z_N, respectively. We compute the bulk and local fixed point renormalizations of the gauge couplings. To this end we extend supergraph techniques to these orbifolds by defining orbifold compatible delta functions. We develop their properties in detail. To cancel the bulk one-loop divergences the bulk gauge kinetic terms and dimension six higher derivative operators are required. The gauge couplings renormalize at the Z_N fixed points due to vector multiplet self interactions; the hyper multiplet renormalizes only non-Z_2 fixed points. In 6D the Wess-Zumino-Witten term and a higher derivative analogue have to renormalize in the bulk as well to preserve 6D gauge invariance.