Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 9, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP09(2014)185
Keywords
Supersymmetric gauge theory; Supersymmetry and Duality; Duality in Gauge Field Theories
Categories
Funding
- Galileo Galilei Institute for Theoretical Physics and INFN
- Simons Center for Geometry and Physics
- Chulalongkorn University
- String Theory Groups of the universities of Rome Tor Vergata and of Oviedo
- STFC Consolidated Grant [ST/J000353/1]
- EPSRC programme [EP/K034456/1]
- ERC
- Short Term Scientific Mission of COST Action [MP1210]
- World Premier International Research Center Initiative (WPI Initiative)
- MEXT, Japan
- INFN
- MIUR-FIRB grant [RBFR10QS5J]
- EPSRC [EP/K034456/1] Funding Source: UKRI
- STFC [ST/J000353/1, ST/L00044X/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/K034456/1] Funding Source: researchfish
- Science and Technology Facilities Council [ST/J000353/1, ST/L00044X/1] Funding Source: researchfish
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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 T rho(G), where rho 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 A(1) 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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