Tρσ(G) theories and their Hilbert series View Full Text


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Article Info

DATE

2015-01

AUTHORS

Stefano Cremonesi, Amihay Hanany, Noppadol Mekareeya, Alberto Zaffaroni

ABSTRACT

We give an explicit formula for the Higgs and Coulomb branch Hilbert series for the class of 3dN=4 superconformal gauge theories Tρσ(G) corresponding to a set of D3 branes ending on NS5 and D5-branes, with or without O3 planes. Here G is a classical group, σ is a partition of G and ρ a partition of the dual group G∨. In deriving such a formula we make use of the recently discovered formula for the Hilbert series of the quantum Coulomb branch of N=4 superconformal theories. The result can be expressed in terms of a generalization of a class of symmetric functions, the Hall-Littlewood polynomials, and can be interpreted in mathematical language in terms of localization. We mainly consider the case G = SU(N) but some interesting results are also given for orthogonal and symplectic groups. More... »

PAGES

150

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/jhep01(2015)150

DOI

http://dx.doi.org/10.1007/jhep01(2015)150

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1048031409


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51 schema:description We give an explicit formula for the Higgs and Coulomb branch Hilbert series for the class of 3dN=4 superconformal gauge theories Tρσ(G) corresponding to a set of D3 branes ending on NS5 and D5-branes, with or without O3 planes. Here G is a classical group, σ is a partition of G and ρ a partition of the dual group G∨. In deriving such a formula we make use of the recently discovered formula for the Hilbert series of the quantum Coulomb branch of N=4 superconformal theories. The result can be expressed in terms of a generalization of a class of symmetric functions, the Hall-Littlewood polynomials, and can be interpreted in mathematical language in terms of localization. We mainly consider the case G = SU(N) but some interesting results are also given for orthogonal and symplectic groups.
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