Monopole operators and Hilbert series of Coulomb branches of 3d N = 4 gauge theories
TLDR
In this paper, the chiral ring and moduli space on the Coulomb branch of an N = 4 superconformal field theory in 2+1 dimensions were identified.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 N = 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 N = 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.read more
Citations
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LieART—A Mathematica application for Lie algebras and representation theory
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TL;DR: LieART 2.0 as mentioned in this paper is an extension of the Mathematica application LieART that supports tensor product decomposition and subalgebra branching of irreducible representations.
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Towards a mathematical definition of Coulomb branches of $3$-dimensional $\mathcal N=4$ gauge theories, II
TL;DR: In this paper, the Coulomb branch is defined as an affine algebraic variety with a singularity and a Coulomb action in the form Ω( √ √ N 2 ).
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Comments on twisted indices in 3d supersymmetric gauge theories
Cyril Closset,Heeyeon Kim +1 more
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3d Coulomb branch and 5d Higgs branch at infinite coupling
TL;DR: In this article, the Coulomb branch of the Higgs branch of minimally supersymmetric five-dimensional SQCD theories was shown to increase in a significant way at the UV fixed point when the inverse gauge coupling is tuned to zero.
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Tropical geometry and five dimensional Higgs branches at infinite coupling
TL;DR: In this paper, a three parameter family of SQCD theories, given by the number of colors Nc for an SU Nc gauge theory, number of fundamental flavors Nf, and the Chern Simons level k, is studied.
References
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Type iib superstrings, bps monopoles, and three-dimensional gauge dynamics
Amihay Hanany,Edward Witten +1 more
TL;DR: In this article, the Coulomb branch of certain three-dimensional supersymmetric gauge theories and the moduli spaces of magnetic monopoles are explained via string theory, and new phase transitions in three dimensions as well as new infrared fixed points and even new coupling constants are predicted from the string theory construction.
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Mirror symmetry in three dimensional gauge theories
TL;DR: In this paper, the authors discuss non-trivial fixed points of the renormalization group with dual descriptions in N = 4 gauge theories in three dimensions and show that small E8 instantons in string theory are described by a local quantum field theory.
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Wilson-'t Hooft operators in four-dimensional gauge theories and S-duality
TL;DR: The Wilson-t Hooft operator as mentioned in this paper is a topologically nontrivial operator that is localized on a straight line, creates electric and magnetic flux, and in the UV limit breaks the conformal invariance in the minimal possible way.
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On Mirror Symmetry in Three Dimensional Abelian Gauge Theories
TL;DR: In this paper, the authors presented an identity relating the partition function of N = 4 supersymmetric QED to that of its dual under mirror symmetry, which is a generalized Fourier transform.
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Topological Disorder Operators in Three-Dimensional Conformal Field Theory
TL;DR: In this paper, a new class of local operators, called monopole operators, which are not polynomial in the fundamental fields and create topological disorder are defined. But they are not a higher-dimensional analogues of twist and winding state operators in free 2D CFTs.