Gaiotto’s Lagrangian Subvarieties via Derived Symplectic Geometry
Victor Ginzburg,Nick Rozenblyum +1 more
TLDR
In this article, a simple interpretation of Gaiotto's construction in terms of derived symplectic geometry is given, 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.Abstract:
Let BunG be the moduli space of G-bundles on a smooth complex projective curve. Motivated by a study of boundary conditions in mirror symmetry, Gaiotto (2016) associated to any symplectic representation of G a Lagrangian subvariety of T∗BunG. 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.read more
Citations
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Cohomological Hall algebra of Higgs sheaves on a curve
TL;DR: The cohomological Hall algebra of the Calabi-Yau category of coherent Higgs sheaves on a smooth projective curve has been studied in this article in the context of Borel-Moore homology.
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Multiplicative Hitchin Systems and Supersymmetric Gauge Theory
Chris Elliott,Vasily Pestun +1 more
TL;DR: In this paper, the multiplicative Hitchin system was shown to be an equivalence of hyperkahler spaces, and the twistor rotation was analyzed for multiplicative Higgs bundles.
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A Taxonomy of Twists of Supersymmetric Yang--Mills Theory
TL;DR: In this article, a complete classification of twisted supersymmetric Yang-Mills theories in dimensions in the dimension of square-zero supercharges in the supersymmetry algebra is given.
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Two-dimensional categorified Hall algebras
Mauro Porta,Francesco Sala +1 more
TL;DR: In this article, Zhao and Kapranov-Vasserot introduced two-dimensional categorified Hall algebras of smooth curves and smooth surfaces, which are associated with suitable derived enhancements of the moduli stack of coherent sheaves.
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Higgs bundles, Lagrangians and mirror symmetry
TL;DR: In this article, a detailed description of the fibres of the G-Hitchin fibration containing generic G0-Higgs bundles, for the real forms G0 = SU* (2m), SO* (4m), and Sp(m, m) of G = SL(2m, C), SO(4m,C) and Sp (m,m), m), respectively, is given.
References
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Shifted Symplectic Structures
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Towards a mathematical definition of Coulomb branches of $3$-dimensional $\mathcal{N}=4$ gauge theories, I
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A Study in Derived Algebraic Geometry, Part 1: Volume I: Correspondences and Duality
Dennis Gaitsgory,Nick Rozenblyum +1 more
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The global nilpotent variety is Lagrangian
TL;DR: In this article, the authors present a short elementary proof of a theorem due to G. Faltings and G. Laumon, which says that the global nilpotent cone is a Lagrangian substack in the cotangent bundle of the moduli space of G-bundles on a complex compact curve.
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Quasi-Hamiltonian reduction via classical Chern–Simons theory
TL;DR: In this paper, the authors put the theory of quasi-Hamiltonian reduction in the framework of shifted symplectic structures developed by Pantev, Toen, Vaquie and Vezzosi.