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Tρσ(G) theories and their Hilbert series.

Cremonesi, Stefano and Hanany, Amihay and Mekareeya, Noppadol and Zaffaroni, Alberto (2015) 'Tρσ(G) theories and their Hilbert series.', Journal of high energy physics., 2015 (01). p. 150.


We give an explicit formula for the Higgs and Coulomb branch Hilbert series for the class of 3d N=4N=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=4N=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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Publisher statement:Open Access, © The Author(s) 2015. 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:07 January 2015
Date deposited:29 March 2017
Date of first online publication:29 January 2015
Date first made open access:No date available

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