Talk page
Title:
Localization on compact spaces, q-W algebras and modularity
Speaker:
Abstract:
The BPS/CFT correspondence allows a wide class of supersymmetric gauge theories to be studied through 2d CFT-like methods. In particular, vortex and instanton partition functions of unitary quiver gauge theories have been identified with chiral correlators or conformal blocks of infinite dimensional symmetry algebras. In this talk, I will discuss three and five dimensional backgrounds, in which cases the relevant algebras are the so-called q-W algebras. When the supersymmetric gauge theories are defined on compact spaces such as the three or five spheres, localization yields partition functions in the form of matrix models exhiniting peculiar modular properties. I will show that these structures can be nicely encoded into the existence of q-W algebras with multiple chiral sectors which are non-trivially fused together through SL(2,Z) or SL(3,Z) elements. As an application, I will explain how these algebraic constructions can be used to confirm or predict new results relating three and five dimensional partiton functions.
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