On 2d TQFTs whose values are holomorphic symplectic varieties

Understand

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.