Real structures on moduli spaces of Higgs bundles

TL;DR

This paper constructs and analyzes real structures on Higgs bundle moduli spaces, revealing their fixed loci as special branes and exploring their topological invariants via advanced K-theory tools.

Contribution

It introduces new commuting real structures on Higgs moduli spaces and characterizes their fixed loci as specific branes, connecting to spectral data and topological invariants.

Findings

Construction of triples of commuting real structures

Identification of fixed loci as (B, A, A), (A, B, A), (A, A, B) branes

Topological invariants described using KO, KR, and equivariant K-theory

Abstract

We construct triples of commuting real structures on the moduli space of Higgs bundles, whose fixed loci are branes of type (B, A, A), (A, B, A) and (A, A, B). We study the real points through the associated spectral data and describe the topological invariants involved using KO, KR and equivariant K-theory.