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Localization on compact spaces, q-W algebras and modularity

Mathematical Physics & Probability

Speaker: Fabrizo Nieri, Uppsala University
Location: 2112 MSB
Start time: Wed, Mar 14 2018, 3:10PM

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.