Tρσ(G) theories and their Hilbert series

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

Abstract

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.

Citation

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. https://doi.org/10.1007/jhep01%282015%29150

• 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
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2015
• Issue: 01
• Article Number: 150
• DOI: https://doi.org/10.1007/jhep01%282015%29150
• Public URL: https://durham-repository.worktribe.com/output/1395162
• Related Public URLs: https://arxiv.org/abs/1410.1548