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Coulomb branch Hilbert series and Hall-Littlewood polynomials

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

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Amihay Hanany

Noppadol Mekareeya

Alberto Zaffaroni


There has been a recent progress in understanding the chiral ring of 3d NN = 4 superconformal gauge theories by explicitly constructing an exact generating function (Hilbert series) counting BPS operators on the Coulomb branch. In this paper we introduce Coulomb branch Hilbert series in the presence of background magnetic charges for flavor symmetries, which are useful for computing the Hilbert series of more general theories through gluing techniques. We find a simple formula of the Hilbert series with background magnetic charges for Tρ(G) theories in terms of Hall-Littlewood polynomials. Here G is a classical group and ρ is a certain partition related to the dual group of G. The Hilbert series for vanishing background magnetic charges show that Coulomb branches of Tρ(G) theories are complete intersections. We also demonstrate that mirror symmetry maps background magnetic charges to baryonic charges.


Cremonesi, S., Hanany, A., Mekareeya, N., & Zaffaroni, A. (2014). Coulomb branch Hilbert series and Hall-Littlewood polynomials. Journal of High Energy Physics, 2014(09), Article 178.

Journal Article Type Article
Acceptance Date Sep 11, 2014
Online Publication Date Sep 30, 2014
Publication Date Sep 30, 2014
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 2014
Issue 09
Article Number 178
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Published Journal Article (945 Kb)

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Copyright Statement
Open Access, © The Author(s) 2014. 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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