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

Cremonesi, Stefano and Hanany, Amihay and Zaffaroni, Alberto (2014) 'Monopole operators and Hilbert series of Coulomb branches of 3d N = 4 gauge theories.', Journal of high energy physics., 2014 (01). 005.


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.

Item Type:Article
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Publisher 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.
Date accepted:10 December 2013
Date deposited:29 March 2017
Date of first online publication:03 January 2014
Date first made open access:29 March 2017

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