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Coulomb branch Hilbert series and three dimensional Sicilian theories.

Cremonesi, Stefano and Hanany, Amihay and Mekareeya, Noppadol and Zaffaroni, Alberto (2014) 'Coulomb branch Hilbert series and three dimensional Sicilian theories.', Journal of high energy physics., 2014 (09). p. 185.


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.

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Publisher 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.
Date accepted:11 September 2014
Date deposited:29 March 2017
Date of first online publication:30 September 2014
Date first made open access:No date available

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