On 2d TQFTs whose values are holomorphic symplectic varieties

Abstract

For simple and simply-connected complex algebraic group G, we conjecture the existence of a functor eta_G from the category of 2-bordisms to the category of holomorphic symplectic varieties with Hamiltonian action, such that gluing of boundaries corresponds to the holomorphic symplectic quotient with respect to the diagonal action of G. We describe various properties of eta_G obtained via string-theoretic analysis. Mathematicians are urged to construct eta_G rigorously.

15 pages, to appear in the proceedings of String-Math 2011 conference; v2: small corrections

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Cited by in corpus (14)

• Infinite Chiral Symmetry in Four Dimensions
• Towards a mathematical definition of Coulomb branches of $3$-dimensional $\mathcal{N}=4$ gauge theories, II
• Tinkertoys for the Twisted D-Series
• Coulomb branch Hilbert series and Three Dimensional Sicilian Theories
• Lagrangian structures on mapping stacks and semi-classical TFTs
• Multiple Derived Lagrangian Intersections
• A review of the T_N theory and its cousins
• 6d $\mathcal{N}=(1,0)$ theories on $T^2$ and class S theories: part I
• Ring objects in the equivariant derived Satake category arising from Coulomb branches (with an appendix by Gus Lonergan)
• Spectral Networks and Snakes
• On the six-dimensional origin of the AGT correspondence
• Representation theory of W-algebras and Higgs branch conjecture
• Four-dimensional N=2 Field Theory and Physical Mathematics
• On 'categories' of quantum field theories