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Three-dimensional N = 4 gauge theories in omega background.

Bullimore, Mathew (2018) 'Three-dimensional N = 4 gauge theories in omega background.', in String-Math 2016 : June 27-July 2, 2016, Collège de France, Paris, France. Providence, Rhode Island: American Mathematical Society, pp. 1-20. Proceedings of symposia in pure mathematics. (98).


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.

Item Type:Book chapter
Full text:(AM) Accepted Manuscript
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Publisher 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.
Date accepted:No date available
Date deposited:11 July 2018
Date of first online publication:June 2018
Date first made open access:No date available

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