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Journal of High Energy Physics

, 2015:150 | Cite as

T ρ σ (G) theories and their Hilbert series

  • Stefano Cremonesi
  • Amihay Hanany
  • Noppadol MekareeyaEmail author
  • Alberto Zaffaroni
Open Access
Regular Article - Theoretical Physics

Abstract

We give an explicit formula for the Higgs and Coulomb branch Hilbert series for the class of 3d \( \mathcal{N}=4 \) superconformal gauge theories T ρ σ (G) corresponding to a set of D3 branes ending on NS5 and D5-branes, with or without O3 planes. Here G is a classical group, σ is a partition of G and ρ a partition of the dual group G . In deriving such a formula we make use of the recently discovered formula for the Hilbert series of the quantum Coulomb branch of \( \mathcal{N}=4 \) superconformal theories. The result can be expressed in terms of a generalization of a class of symmetric functions, the Hall-Littlewood polynomials, and can be interpreted in mathematical language in terms of localization. We mainly consider the case G = SU(N) but some interesting results are also given for orthogonal and symplectic groups.

Keywords

Supersymmetric gauge theory Supersymmetry and Duality Brane Dynamics in Gauge Theories Duality in Gauge Field Theories 

Notes

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) 2015

Authors and Affiliations

  • Stefano Cremonesi
    • 1
    • 2
  • Amihay Hanany
    • 2
  • Noppadol Mekareeya
    • 3
    Email author
  • Alberto Zaffaroni
    • 4
    • 5
  1. 1.Department of MathematicsKing’s College LondonLondonU.K.
  2. 2.Theoretical Physics GroupImperial College LondonLondonU.K.
  3. 3.Theory Division, Physics DepartmentCERNGeneva 23Switzerland
  4. 4.Dipartimento di FisicaUniversità di Milano-BicoccaMilanoItaly
  5. 5.INFN, sezione di Milano-BicoccaMilanoItaly

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