W-algebras associated to surfaces

Abstract

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

References in corpus (2)

• Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces
• AGT relations for sheaves on surfaces

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