Index formula for Hamiltonian loop group spaces

TL;DR

This paper develops index formulas for Hamiltonian loop group spaces using K-theory and Fredholm complexes, with applications to gauge theory and moduli spaces of flat connections.

Contribution

It introduces equivariant index formulas for Hamiltonian loop group spaces and connects them to gauge theory via non-local elliptic boundary value problems.

Findings

Derived new equivariant index formulas for Hamiltonian loop group spaces.

Established a gauge theory analogue of the Teleman-Woodward index formula.

Linked K-theory classes with moduli spaces of flat connections.

Abstract

We study K-theory classes of Hamiltonian loop group spaces represented by admissible Fredholm complexes. We prove various equivariant index formulae in this context. In a sequel to this article we show that, when specialized to a family of non-local elliptic boundary value problems over the moduli space of framed flat connections on a surface, one obtains a gauge theory analogue of the Teleman-Woodward index formula.