Branes in the moduli space of framed instantons

Abstract

In the physicist's language, a brane in a hyperkahler manifold is a submanifold which is either complex or lagrangian with respect to three Kahler structures of the ambient manifold. By considering the fixed loci of certain involutions, we describe branes in Nakajima quiver varieties of all possible types. We then focus on the moduli space of framed torsion free sheaves on the projective plane, showing how the involutions considered act on sheaves, and proving the existence of branes in some cases.

References in corpus (3)

• Lectures on Nakajima's Quiver Varieties
• Symplectic bundles on the plane, secant varieties and Lüroth quartics revisited
• Orthogonal bundles and skew-Hamiltonian matrices

Cited by in corpus (9)

• Singular Geometry and Higgs Bundles in String Theory
• Moduli spaces of generalized hyperpolygons
• Mirror symmetry for Nahm branes
• Parallels between moduli of quiver representations and vector bundles over curves
• Brane involutions on irreducible holomorphic symplectic manifolds
• The Kapustin-Witten equations and nonabelian Hodge theory
• Group actions on quiver varieties and applications
• Torsion free instanton sheaves on the blow-up of ${\mathbb{P}}^n$ at a point
• Torsion free instanton sheaves on the blow-up of ${\mathbb{P}}^3$ at a point