Abstract
We construct an ϵ-deformation of W algebras, corresponding to the additive version of quiver algebras which feature prominently in the 5D version of the BPS/CFT correspondence and refined topological strings on toric Calabi–Yau’s. This new type of algebras fill in the missing intermediate level between q-deformed and ordinary W algebras. We show that ϵ-deformed W algebras are spectral duals of conventional W algebras, in particular the ϵ-deformed conformal blocks manifestly reproduce instanton partition functions of 4D quiver gauge theories in the full Ω-background and give dual integral representations of ordinary W conformal blocks.
Highlights
Any quantum field theory gives rise to an algebra of operators acting on its Hilbert space
We show that -deformed W algebras are spectral duals of conventional W algebras, in particular the deformed conformal blocks manifestly reproduce instanton partition functions of 4D N = 2 quiver gauge theories in the full Ω-background and give dual integral representations of ordinary W conformal blocks
We have introduced a class of algebras which are naturally associated to any 4D N = 2 quiver gauge theory with unitary groups
Summary
Any quantum field theory gives rise to an algebra of operators acting on its Hilbert space. The virtue of supersymmetric gauge theories is that for a certain BPS subsector of the Hilbert space, the algebra can often be written explicitly. For 4D N = 2 quiver gauge theories, the main focus of this paper, the space of supersymmetric states is described by the (equivariant) cohomology of instanton moduli spaces [1,2,3,4,5,6]. The resulting algebra describes the action of certain correspondences on the cohomology and is known as the spherical Hecke algebra or affine
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