Coulomb branch Hilbert series and Hall-Littlewood polynomials

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

Abstract

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.

Citation

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. https://doi.org/10.1007/jhep09%282014%29178

• 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
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2014
• Issue: 09
• Article Number: 178
• DOI: https://doi.org/10.1007/jhep09%282014%29178
• Public URL: https://durham-repository.worktribe.com/output/1387091
• Related Public URLs: https://arxiv.org/abs/1403.0585