Algebraic properties of the monopole formula

Amihay Hanany; Marcus Sperling

doi:10.1007/JHEP02(2017)023

Algebraic properties of the monopole formula

Amihay Hanany (Corresponding author)
, Marcus Sperling

Mathematical Physics

Publications: Contribution to journal › Article › Peer Reviewed

Abstract

The monopole formula provides the Hilbert series of the Coulomb branch for a 3-dimensional N= 4 gauge theory. Employing the concept of a fan defined by the matter content, and summing over the corresponding collection of monoids, allows the following: firstly, we provide explicit expressions for the Hilbert series for any gauge group. Secondly, we prove that the order of the pole at t = 1 and t → ∞ equals the complex or quaternionic dimension of the moduli space, respectively. Thirdly, we determine all bare and dressed BPS monopole operators that are sufficient to generate the entire chiral ring. As an application, we demonstrate the implementation of our approach to computer algebra programs and the applicability to higher rank gauge theories.

Original language	English
Article number	23
Number of pages	43
Journal	Journal of High Energy Physics
Volume	2017
Issue number	2
DOIs	https://doi.org/10.1007/JHEP02(2017)023
Publication status	Published - 6 Feb 2017

Funding

We thank Simon Brandhorst, Santiago Cabrera, Bo Feng, Giulia Ferlito, Yang-Hui He, Rudolph Kalveks, and Zhenghao Zhong for useful discussions. A. H. is supported by STFC Consolidated Grant STJ00035331, and EPSRC Programme Grant EP/K034456/1. M. S. was supported by the DFG research training group GRK1463 "Analysis, Geometry, and String Theory" and the Institut fur Theoretische Physik of the Leibniz Universitat Hannover. M. S. is currently supported by Austrian Science Fund (FWF) grant P28590.

Austrian Fields of Science 2012

103012 High energy physics

Keywords

Field Theories in Lower Dimensions
Supersymmetric gauge theory
GAUGE-THEORIES

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10.1007/JHEP02(2017)023Licence: CC BY 4.0

http://phaidra.univie.ac.at/o:877100Licence: CC BY 4.0

Cite this

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title = "Algebraic properties of the monopole formula",

abstract = "The monopole formula provides the Hilbert series of the Coulomb branch for a 3-dimensional N= 4 gauge theory. Employing the concept of a fan defined by the matter content, and summing over the corresponding collection of monoids, allows the following: firstly, we provide explicit expressions for the Hilbert series for any gauge group. Secondly, we prove that the order of the pole at t = 1 and t → ∞ equals the complex or quaternionic dimension of the moduli space, respectively. Thirdly, we determine all bare and dressed BPS monopole operators that are sufficient to generate the entire chiral ring. As an application, we demonstrate the implementation of our approach to computer algebra programs and the applicability to higher rank gauge theories.",

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N2 - The monopole formula provides the Hilbert series of the Coulomb branch for a 3-dimensional N= 4 gauge theory. Employing the concept of a fan defined by the matter content, and summing over the corresponding collection of monoids, allows the following: firstly, we provide explicit expressions for the Hilbert series for any gauge group. Secondly, we prove that the order of the pole at t = 1 and t → ∞ equals the complex or quaternionic dimension of the moduli space, respectively. Thirdly, we determine all bare and dressed BPS monopole operators that are sufficient to generate the entire chiral ring. As an application, we demonstrate the implementation of our approach to computer algebra programs and the applicability to higher rank gauge theories.

AB - The monopole formula provides the Hilbert series of the Coulomb branch for a 3-dimensional N= 4 gauge theory. Employing the concept of a fan defined by the matter content, and summing over the corresponding collection of monoids, allows the following: firstly, we provide explicit expressions for the Hilbert series for any gauge group. Secondly, we prove that the order of the pole at t = 1 and t → ∞ equals the complex or quaternionic dimension of the moduli space, respectively. Thirdly, we determine all bare and dressed BPS monopole operators that are sufficient to generate the entire chiral ring. As an application, we demonstrate the implementation of our approach to computer algebra programs and the applicability to higher rank gauge theories.

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KW - GAUGE-THEORIES

UR - https://arxiv.org/abs/1611.07030

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JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

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ER -

Algebraic properties of the monopole formula

Abstract

Funding

Austrian Fields of Science 2012

Keywords

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