Instantons in Partially Broken Gauge Groups

TL;DR

This paper explores how instantons in partially broken gauge groups influence low-energy effective theories, emphasizing the importance of the embedding index and homotopy groups in identifying such instantons.

Contribution

It provides a detailed analysis of instantons in partially broken gauge groups, introducing criteria based on the embedding index and homotopy groups, with examples in supersymmetric theories.

Findings

Instantons can exist in broken gauge sectors affecting low-energy physics.

The embedding index and c_3(G/H) determine instanton presence.

Supersymmetric examples illustrate these effects.

Abstract

We discuss the effects of instantons in partially broken gauge groups on the low-energy effective gauge theory. Such effects arise when some of the instantons of the original gauge group G are no longer contained in (or can not be gauge rotated into) the unbroken group H. In cases of simple G and H, a good indicator for the existence of such instantons is the ``index of embedding.'' However, in the general case one has to examine \pi_3(G/H) to decide whether there are any instantons in the broken part of the gauge group. We give several examples of supersymmetric theories where such instantons exist and leave their effects on the low-energy effective theory.