On non-connected simple linear groups with a free algebra of invariants

Shmelkin, D. A.

doi:10.1070/im1996v060n04abeh000081

Cited by 4 publications

(2 citation statements)

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“…17 In retrospect one can check in the mathematical literature that whenever one considers disconnected groups, very frequently the ring of invariants stops being freely generated. In fact, using [39,40], one can see that the principal extension groups SU(N ) must indeed produce non freely generated rings in the adjoint for N > 4. Indeed, the criterion for the ring to be freely generated is that the component group Γ should act by reflections (a symmetry with codimension one kernel) on the invariant ring of the connected components.…”

Section: The Non-freely Generated Coulomb Branchmentioning

confidence: 99%

Gauge theories from principally extended disconnected gauge groups

Bourget

Pini²,

Rodrı́guez-Gómez

2019

Nuclear Physics B

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We introduce gauge theories based on a class of disconnected gauge groups, called principal extensions. Although in this work we focus on 4d theories with N = 2 SUSY, such construction is independent of spacetime dimensions and supersymmetry. These groups implement in a consistent way the discrete gauging of charge conjugation, for arbitrary rank. Focusing on the principal extension of SU(N ), we explain how many of the exact methods for theories with 8 supercharges can be put into practice in that context. We then explore the physical consequences of having a disconnected gauge group: we find that the Coulomb branch is generically non-freely generated, and the global symmetry of the Higgs branch is modified in a non-trivial way.

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