Abstract
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 mathcal{N} = 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.
Highlights
Supersymmetric gauge theories with 8 supercharges are central objects in string theory and quantum field theory
Examples include nilpotent orbit closures of the exceptional E-type algebras and magnetic quivers that arise from brane physics
Due to the high amount of supersymmetry (SUSY), there are some families in which the field theory ingredients such as the gauge groups, matter content, and the superpotential interactions can be neatly encoded in so-called quiver diagrams [1, 2]
Summary
Supersymmetric gauge theories with 8 supercharges are central objects in string theory and quantum field theory. When studying the moduli space of unitary quivers derived from brane configurations [38], there always exists a trivially acting diagonal U(1)diag which may or may not be a subgroup of the gauge group. This U(1) describes the center of mass. That acts trivially on the matter content, the choice of GH or G affects the magnetic lattice and the moduli space This is supported by explicit Hilbert series computations. We present Coulomb branch Hilbert series of various families of unitary-orthosymplectic quiver theories where H equals the kernel of.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.