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Monopole operators and Hilbert series of Coulomb branches of 3d N = 4 gauge theories

Cremonesi, Stefano; Hanany, Amihay; Zaffaroni, Alberto

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Authors

Amihay Hanany

Alberto Zaffaroni



Abstract

This paper addresses a long standing problem - to identify the chiral ring and moduli space (i.e. as an algebraic variety) on the Coulomb branch of an NN = 4 superconformal field theory in 2+1 dimensions. Previous techniques involved a computation of the metric on the moduli space and/or mirror symmetry. These methods are limited to sufficiently small moduli spaces, with enough symmetry, or to Higgs branches of sufficiently small gauge theories. We introduce a simple formula for the Hilbert series of the Coulomb branch, which applies to any good or ugly three-dimensional NN = 4 gauge theory. The formula counts monopole operators which are dressed by classical operators, the Casimir invariants of the residual gauge group that is left unbroken by the magnetic flux. We apply our formula to several classes of gauge theories. Along the way we make various tests of mirror symmetry, successfully comparing the Hilbert series of the Coulomb branch with the Hilbert series of the Higgs branch of the mirror theory.

Citation

Cremonesi, S., Hanany, A., & Zaffaroni, A. (2014). Monopole operators and Hilbert series of Coulomb branches of 3d N = 4 gauge theories. Journal of High Energy Physics, 2014(01), Article 005. https://doi.org/10.1007/jhep01%282014%29005

Journal Article Type Article
Acceptance Date Dec 10, 2013
Online Publication Date Jan 3, 2014
Publication Date Jan 3, 2014
Deposit Date Feb 2, 2017
Publicly Available Date Mar 28, 2024
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2014
Issue 01
Article Number 005
DOI https://doi.org/10.1007/jhep01%282014%29005
Related Public URLs https://arxiv.org/abs/1309.2657

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Published Journal Article (605 Kb)
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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

Copyright Statement
Open Access, © The Author(s) 2014. Article funded by SCOAP3. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.





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