Gaiotto's Lagrangian subvarieties via derived symplectic geometry

Victor Ginzburg; Nick Rozenblyum

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arXiv · 1703.08578

Gaiotto's Lagrangian subvarieties via derived symplectic geometry

Victor Ginzburg·Nick Rozenblyum

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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.

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Victor Ginzburg, Nick Rozenblyum. 2017-03-24. Gaiotto's Lagrangian subvarieties via derived symplectic geometry. https://arxiv.org/abs/1703.08578

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