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Durham University

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Publication details for Mathew Bullimore

Bullimore, Mathew (2018), Three-Dimensional N = 4 Gauge Theories in Omega Background, in Kashani-Poor, Amir-Kian, Minasian, Ruben, Nekrasov, Nikita & Pioline, Boris eds, Proceedings of Symposia in Pure Mathematics 98: String-Math 2016. Paris, France, American Mathematical Society, Providence, Rhode Island, 1-20.

Author(s) from Durham


We review the description of three-dimensional gauge theories with N = 4 supersymmetry in the presence of an omega background as an N = 4 supersymmetric quantum mechanics. We will focus throughout on a simple abelian example. The Hilbert space of supersymmetric ground states is
populated by generalized vortex con gurations, while half-BPS monopole operators act on the Hilbert space by creating and annihilating vortices, furnishing it with the structure of a Verma module for the quantized Coulomb branch chiral ring. Furthermore, by introducing two-dimensional N = (2; 2) boundary conditions, we nd a nite version of the AGT correspondence between vortex partition functions and overlaps of Whittaker vectors for quantized Coulomb branch chiral rings.