Spinors, Lagrangians and rank 2 Higgs bundles

Abstract

The paper considers the Dirac operator on a Riemann surface coupled to a symplectic holomorphic vector bundle W. Each spinor in the null-space generates through the moment map a Higgs bundle, and varying W one obtains a holomorphic Lagrangian subvariety in the moduli space of Higgs bundles. Applying this to the irreducible symplectic representations of SL(2) we obtain Lagrangian submanifolds of the rank 2 moduli space which link up with m-period points on the Prym variety of the spectral curve as well as Brill-Noether loci on the moduli space of semistable bundles. The case of genus 2 is investigated in some detail.

31 pages

References in corpus (1)

• Bohr--Sommerfeld Lagrangians of moduli spaces of Higgs bundles

Cited by in corpus (7)

• Singular Geometry and Higgs Bundles in String Theory
• Unramified covers and branes on the Hitchin system
• Branes on the singular locus of the Hitchin system via Borel and other parabolic subgroups
• Mirror symmetry for Nahm branes
• Gaiotto's Lagrangian subvarieties via derived symplectic geometry
• Gaiotto's Lagrangian subvarieties via loop groups
• A Note on Coupled Dirac Operators