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Tρσ(G) theories and their Hilbert series

Cremonesi, Stefano; Hanany, Amihay; Mekareeya, Noppadol; Zaffaroni, Alberto

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Amihay Hanany

Noppadol Mekareeya

Alberto Zaffaroni


We give an explicit formula for the Higgs and Coulomb branch Hilbert series for the class of 3d N=4N=4 superconformal gauge theories Tρσ(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 N=4N=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.


Cremonesi, S., Hanany, A., Mekareeya, N., & Zaffaroni, A. (2015). Tρσ(G) theories and their Hilbert series. Journal of High Energy Physics, 2015(01), Article 150.

Journal Article Type Article
Acceptance Date Jan 7, 2015
Online Publication Date Jan 29, 2015
Publication Date Jan 29, 2015
Deposit Date Feb 2, 2017
Publicly Available Date Mar 29, 2017
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2015
Issue 01
Article Number 150
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Published Journal Article (845 Kb)

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Copyright Statement
Open Access, © The Author(s) 2015. 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.

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