2020/07/31 by Antoine Bourget, Julius F. Grimminger, Amihay Hanany +3 · 38 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #BRST quantization #Black Holes and Theoretical Physics #Gauge group #Gauge theory #Group (periodic table) #Higgs boson #Hilbert–Poincaré series #Magnetic monopole #Moduli space #Quantum Chromodynamics and Particle Interactions #Quiver #Supersymmetric gauge theory #hep-th
paper · pdf · doi:10.1007/jhep12(2020)092
published in Journal of High Energy Physics 2020(12) (Springer Nature) · v2: 44 pages + appendices, matches JHEP version, added references and fixed typos
openalex created_date 2020/07/16 · openalex publication_date 2020/12/01 · arxiv created 2020/12/14 · arxiv updated 2020/12/30 · openalex updated_date 2026/08/05
A bstract For any gauge theory, there may be a subgroup of the gauge group which acts trivially on the matter content. While many physical observables are not sensitive to this fact, the choice of the precise gauge group becomes crucial when the magnetic lattice of the theory is considered. This question is addressed in the context of Coulomb branches for 3d N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 quiver gauge theories, which are moduli spaces of dressed monopole operators. We compute the Coulomb branch Hilbert series of many unitary-orthosymplectic quivers for different choices of gauge groups, including diagonal quotients of the product gauge group of individual factors, where the quotient is by a trivially acting subgroup. Choosing different such diagonal groups results in distinct Coulomb branches, related as orbifolds. Examples include nilpotent orbit closures of the exceptional E-type algebras and magnetic quivers that arise from brane physics. This includes Higgs branches of theories with 8 supercharges in dimensions 4, 5, and 6. A crucial ingredient in the calculation of exact refined Hilbert series is the alternative construction of unframed magnetic quivers from resolved Slodowy slices, whose Hilbert series can be derived from Hall-Littlewood polynomials.