Higgs bundles and (A,B,A)-branes

TL;DR

This paper constructs and analyzes (A,B,A)-branes in moduli spaces of G_c-Higgs bundles on Riemann surfaces, revealing their structure as real integrable systems through spectral data.

Contribution

It introduces a new method to construct (A,B,A)-branes via anti-holomorphic involutions and studies their geometric properties and integrable system structure.

Findings

(A,B,A)-branes form real integrable systems

Spectral data characterizes the geometry of these branes

Construction method applies to various G_c-Higgs bundle moduli spaces

Abstract

Through the action of anti-holomorphic involutions on a compact Riemann surface, we construct families of (A,B,A)-branes in the moduli spaces of G_c-Higgs bundles on the Riemann surface. We study the geometry of these (A,B,A)-branes in terms of spectral data and show they have the structure of real integrable systems.