We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham Research Online
You are in:

Coulomb branch Hilbert series and Hall-Littlewood polynomials.

Cremonesi, Stefano and Hanany, Amihay and Mekareeya, Noppadol and Zaffaroni, Alberto (2014) 'Coulomb branch Hilbert series and Hall-Littlewood polynomials.', Journal of high energy physics., 2014 (09). p. 178.


There has been a recent progress in understanding the chiral ring of 3d NN = 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 Tρ(G) theories in terms of Hall-Littlewood polynomials. Here G is a classical group and ρ is a certain partition related to the dual group of G. The Hilbert series for vanishing background magnetic charges show that Coulomb branches of Tρ(G) theories are complete intersections. We also demonstrate that mirror symmetry maps background magnetic charges to baryonic charges.

Item Type:Article
Full text:(VoR) Version of Record
Available under License - Creative Commons Attribution.
Download PDF
Publisher Web site:
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

Save or Share this output

Look up in GoogleScholar