On 2d TQFTs whose values are holomorphic symplectic varieties

2011/06/28 by Gregory W. Moore, Yuji Tachikawa, Moore, Gregory W. +1 · 7 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1106.5698

openalex publication_date 2011/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Wall-crossing, Hitchin Systems, and the WKB Approximation
• The gravity duals of N=2 superconformal field theories

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