Narasimhan--Ramanan branes and wobbly Higgs bundles

TL;DR

This paper investigates the geometric properties of Narasimhan--Ramanan branes within the moduli space of Higgs bundles, revealing their intersection with wobbly Higgs bundles and exploring mirror symmetry conjectures.

Contribution

The authors demonstrate that the support of Narasimhan--Ramanan branes intersects non-trivially with the locus of wobbly Higgs bundles, providing new insights into their geometric structure.

Findings

Support of branes intersects wobbly Higgs bundles

Provides evidence for mirror symmetry conjectures

Advances understanding of Higgs bundle moduli space

Abstract

Narasimhan--Ramanan branes were introduced by the authors in a previous article. They consist of a family of $BBB$-branes inside the moduli space of Higgs bundles, and a family of complex Lagrangian subvarieties. It was conjectured that these complex Lagrangian subvarieties support the $BAA$-branes that are mirror dual to the Narasimhan--Ramanan $BBB$-branes. In this article we show that the support of these branes intersects non-trivially the locus of wobbly Higgs bundles.