Coulomb branch Hilbert series and Hall-Littlewood polynomials

被引:57
作者
Cremonesi, Stefano [1 ]
Hanany, Amihay [1 ]
Mekareeya, Noppadol [2 ]
Zaffaroni, Alberto [3 ,4 ]
机构
[1] Univ London Imperial Coll Sci Technol & Med, Theoret Phys Grp, London SW7 2AZ, England
[2] CERN, Div Theory, Dept Phys, CH-1211 Geneva 23, Switzerland
[3] Univ Milano Bicocca, Dipartimento Fis, I-20126 Milan, Italy
[4] Ist Nazl Fis Nucl, Sez Milano Bicocca, I-20126 Milan, Italy
基金
英国工程与自然科学研究理事会;
关键词
Supersymmetric gauge theory; Supersymmetry and Duality; Duality in Gauge Field Theories; GAUGE-THEORIES;
D O I
10.1007/JHEP09(2014)178
中图分类号
O412 [相对论、场论]; O572.2 [粒子物理学];
学科分类号
摘要
There has been a recent progress in understanding the chiral ring of 3d N = 4 superconformal gauge theories by explicitly constructing an exact generating function (Hilbert series) counting BPS operators on the Coulomb branch. In this paper we introduce Coulomb branch Hilbert series in the presence of background magnetic charges for flavor symmetries, which are useful for computing the Hilbert series of more general theories through gluing techniques. We find a simple formula of the Hilbert series with background magnetic charges for T-rho(G) theories in terms of Hall-Littlewood polynomials. Here G is a classical group and rho is a certain partition related to the dual group of G. The Hilbert series for vanishing background magnetic charges show that Coulomb branches of T-rho(G) theories are complete intersections. We also demonstrate that mirror symmetry maps background magnetic charges to baryonic charges.
引用
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页数:59
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