W$W$‐algebras associated to surfaces
Copyright policy )W$W$‐algebras associated to surfaces
We define an integral form of the deformed W-algebra of type gl_r, and construct its action on the K-theory groups of moduli spaces of rank r stable sheaves on a smooth projective surface S, under certain assumptions. Our construction generalizes the action studied by Nakajima, Grojnowski and Baranovsky in cohomology, although the appearance of deformed W-algebras by generators and relations is a new feature. Physically, this action encodes the AGT correspondence for 5d supersymmetric gauge theory on S x circle.
typos fixed, presentation style improved
- Massachusetts Institute of Technology United States
Mathematics - Algebraic Geometry, 14J60, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Algebraic Geometry (math.AG)
Mathematics - Algebraic Geometry, 14J60, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Algebraic Geometry (math.AG)
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