Instanton moduli spaces and $\mathcal{W}$-algebras

Abstract

We describe the (equivariant) intersection cohomology of certain moduli spaces ("framed Uhlenbeck spaces") together with some structures on them (such as e.g.\ the Poincaré pairing) in terms of representation theory of some vertex operator algebras ("$\mathcal{W}$-algebras").

117 pages; v2, 120 pages, definition of the inner product corrected; v3, 122 pages, definition of hyperbolic semi-smallness is added; v4, 124 pages, edited according to the referee's suggestion; v5, 122 pages, reformatted with smfart.cls so that numberings are the same as published version

References in corpus (2)

• Asymptotically free N=2 theories and irregular conformal blocks
• On a theorem of Braden

Cited by in corpus (21)

• Webs of W-algebras
• Coulomb branches of $3d$ $\mathcal{N}=4$ quiver gauge theories and slices in the affine Grassmannian (with appendices by Alexander Braverman, Michael Finkelberg, Joel Kamnitzer, Ryosuke Kodera, Hiraku Nakajima, Ben Webster, and Alex Weekes)
• Quiver Yangian and Supersymmetric Quantum Mechanics
• Duality walls and defects in 5d N=1 theories
• M-theory in the Omega-background and 5-dimensional non-commutative gauge theory
• Triality in Little String Theories
• On Extensions of $\widehat{\mathfrak{gl}(m|n)}$ Kac-Moody algebras and Calabi-Yau Singularities
• ADE Little String Theory on a Riemann Surface (and Triality)
• A brief review of the 2d/4d correspondences
• Vertex Algebras at the Corner
• Quantum q-Langlands Correspondence
• Questions on provisional Coulomb branches of $3$-dimensional $\mathcal{N}=4$ gauge theories
• Towards geometric Satake correspondence for Kac-Moody algebras -- Cherkis bow varieties and affine Lie algebras of type $A$
• Norm of the Whittaker vector of the deformed Virasoro algebra
• Super Topological Recursion and Gaiotto Vectors For Superconformal Blocks
• Cherkis bow varieties and Coulomb branches of quiver gauge theories of affine type $A$
• Equivariant localization in factorization homology and applications in mathematical physics I: Foundations
• On 'categories' of quantum field theories
• String Theory and Math: Why This Marriage May Last
• Generalized orbital varieties for Mirkovic-Vybornov slices as affinizations of Mirkovic-Vilonen cycles
• Singular Vector of Ding-Iohara-Miki Algebra and Hall-Littlewood Limit of 5D AGT Conjecture