Narasimhan–Ramanan branes and wobbly Higgs bundles

Abstract

Narasimhan–Ramanan branes, introduced by the authors in a previous paper, consist of a family of $\mathrm{\text{BBB}}$-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 $\mathrm{\text{BBB}}$-branes that are mirror dual to the Narasimhan–Ramanan $\mathrm{\text{BBB}}$-branes. In this paper, we show that the support of these branes intersects nontrivially the locus of wobbly Higgs bundles.