Quiver theories and formulae for Slodowy slices of classical algebras

Cabrera, Santiago  (Theoretical Physics Group, The Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom) ; Hanany, Amihay (Theoretical Physics Group, The Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom) ; Kalveks, Rudolph  (Theoretical Physics Group, The Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom)

21 December 2018

Abstract: We utilise SUSY quiver gauge theories to compute properties of Slodowy slices; these are spaces transverse to the nilpotent orbits of a Lie algebra g . We analyse classes of quiver theories, with Classical gauge and flavour groups, whose Higgs branch Hilbert series are the intersections between Slodowy slices and the nilpotent cone S∩N of g . We calculate refined Hilbert series for Classical algebras up to rank 4 (and A5 ), and find descriptions of their representation matrix generators as algebraic varieties encoding the relations of the chiral ring. We also analyse a class of dual quiver theories, whose Coulomb branches are intersections S∩N ; such dual quiver theories exist for the Slodowy slices of A algebras, but are limited to a subset of the Slodowy slices of BCD algebras. The analysis opens new questions about the extent of 3 d mirror symmetry within the class of SCFTs known as Tσρ(G) theories. We also give simple group theoretic formulae for the Hilbert series of Slodowy slices; these draw directly on the SU(2) embedding into G of the associated nilpotent orbit, and the Hilbert series of the nilpotent cone.


Published in: Nuclear Physics B 939 (2019) 308-357
Published by: Elsevier
DOI: 10.1016/j.nuclphysb.2018.12.022
License: CC-BY-3.0



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