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Three-Dimensional N = 4 Gauge Theories in Omega Background

Bullimore, Mathew

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Authors



Contributors

Amir-Kian Kashani-Poor
Editor

Ruben Minasian
Editor

Nikita Nekrasov
Editor

Boris Pioline
Editor

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 Mar 28, 2024
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/

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Accepted Conference Proceeding (402 Kb)
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Copyright Statement
© 2018 American Mathematical Society. First published in String-Math 2016, Proceedings of Symposia in Pure Mathematics in 98, 2018, published by the American Mathematical Society.





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