On 2d TQFTs whose values are holomorphic symplectic varieties

TL;DR

This paper conjectures a functor from 2-dimensional bordisms to holomorphic symplectic varieties for complex algebraic groups, linking topological quantum field theories with complex geometry, and discusses properties derived from string theory.

Contribution

It introduces a conjectural functor eta_G connecting 2d TQFTs to holomorphic symplectic varieties, proposing a new geometric framework for TQFTs associated with complex algebraic groups.

Findings

Proposes a conjectural functor eta_G for simple, simply-connected groups

Describes properties of eta_G derived from string-theoretic analysis

Urges mathematicians to rigorously construct eta_G

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.