An index for confined monopoles

TL;DR

This paper develops a new index formula for fluctuation operators in N=2 SQCD with non-abelian confined multimonopoles, linking topological charges to the moduli space dimension.

Contribution

It generalizes classical index calculations to complex backgrounds, providing a topological index for confined multimonopoles in supersymmetric gauge theories.

Findings

Derived an index formula for non-abelian confined multimonopoles.

Connected the index to topological charges and moduli space dimension.

Extended classical index theorems to new nontrivial backgrounds.

Abstract

We compute the index and associated spectral density for fluctuation operators which are defined via the Lagrangian of N=2 SQCD in the background of non-abelian confined multimonopoles. To this end we generalize the standard index calculations of Callias and Weinberg to the case of asymptotically nontrivial backgrounds. The resulting index is determined by topological charges. We conjecture that this index counts one quarter of the dimension of the moduli space of confined multimonopoles.