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Coulomb branch Hilbert series and three dimensional Sicilian theories

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

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Authors

Amihay Hanany

Noppadol Mekareeya

Alberto Zaffaroni



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
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
Related Public URLs https://arxiv.org/abs/1403.2384

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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

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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