Three-Dimensional N = 4 Gauge Theories in Omega Background

Bullimore, Mathew

Abstract

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 congurations, 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.

Citation

Bullimore, M. (2018). Three-Dimensional N = 4 Gauge Theories in Omega Background. In A. Kashani-Poor, R. Minasian, N. Nekrasov, & B. Pioline (Eds.), String-Math 2016 : June 27-July 2, 2016, Collège de France, Paris, France (1-20)

• Conference Name: String-Math 2016
• Conference Location: Paris, France
• Start Date: Jun 27, 2023
• End Date: Jul 2, 2016
• Publication Date: Jun 1, 2018
• Deposit Date: Jul 11, 2018
• Publicly Available Date: Jul 11, 2018
• Publisher: American Mathematical Society
• Pages: 1-20
• Series Title: Proceedings of symposia in pure mathematics
• Series Number: 98
• Book Title: String-Math 2016 : June 27-July 2, 2016, Collège de France, Paris, France.
• ISBN: 9781470435158
• Public URL: https://durham-repository.worktribe.com/output/1145281
• Publisher URL: https://bookstore.ams.org/pspum-98/