Journal of High Energy Physics

, 2017:23 | Cite as

Algebraic properties of the monopole formula

Open Access
Regular Article - Theoretical Physics


The monopole formula provides the Hilbert series of the Coulomb branch for a 3-dimensional \( \mathcal{N}=4 \) 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.


Field Theories in Lower Dimensions Supersymmetric gauge theory 


Open Access

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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Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Theoretical Physics GroupImperial College LondonLondonU.K.
  2. 2.Fakultät für PhysikUniversität WienWienAustria

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