On 2d TQFTs whose values are holomorphic symplectic varieties

摘要

For a simple and simply-connected complex algebraic group G_c, we conjecture the existence of a functor ηG_c 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_c. We describe various properties of ηG_c obtained via string-theoretic analysis. Mathematicians are urged to construct ηG_c rigorously.