Gaiotto's Lagrangian subvarieties via derived symplectic geometry

Abstract

Let Bun_G be the moduli space of G-bundles on a smooth complex projective curve. Motivated by a study of boundary conditions in mirror symmetry, D. Gaiotto associated to any symplectic representation of G a Lagrangian subvariety of the cotangent bundle of Bun_G. We give a simple interpretation of (a generalization of) Gaiotto's construction in terms of derived symplectic geometry. This allows to consider a more general setting where symplectic G-representations are replaced by arbitrary symplectic manifolds equipped with a Hamiltonian G-action and with an action of the multiplicative group that rescales the symplectic form with positive weight.

Final version

References in corpus (2)

• Shifted cotangent stacks are shifted symplectic
• Shifted Symplectic and Poisson Structures on Spaces of Framed Maps

Cited by in corpus (1)

• Gaiotto's Lagrangian subvarieties via loop groups