Coulomb branch Hilbert series and three dimensional Sicilian theories

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

Abstract

We evaluate the Coulomb branch Hilbert series of mirrors of three dimensional Sicilian theories, which arise from compactifying the 6d (2, 0) theory with symmetry G on a circle times a Riemann surface with punctures. We obtain our result by gluing together the Hilbert series for building blocks Tρ(G), where ρ is a certain partition related to the dual group of G, which we evaluated in a previous paper. The result is expressed in terms of a class of symmetric functions, the Hall-Littlewood polynomials. As expected from mirror symmetry, our results agree at genus zero with the superconformal index prediction for the Higgs branch Hilbert series of the Sicilian theories and extend it to higher genus. In the A1 case at genus zero, we also evaluate the Coulomb branch Hilbert series of the Sicilian theory itself, showing that it only depends on the number of external legs.

Citation

Cremonesi, S., Hanany, A., Mekareeya, N., & Zaffaroni, A. (2014). Coulomb branch Hilbert series and three dimensional Sicilian theories. Journal of High Energy Physics, 2014(09), Article 185. https://doi.org/10.1007/jhep09%282014%29185

• 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: 185
• DOI: https://doi.org/10.1007/jhep09%282014%29185
• Public URL: https://durham-repository.worktribe.com/output/1366068
• Related Public URLs: https://arxiv.org/abs/1403.2384