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We provide a solution in case the gauge group is a torus.
The results are generalized to theories with SO(N) gauge group.
An action of the gauge group having this property is called (k+1 -fold transitive.
Arveson has characterized completely the gauge group of E0-semigroups of type I, and as a consequence it is known that in this case the gauge group action is transitive.
The gauge group of a spatial E0-semigroup has a natural action on the set of units by operator multiplication.
Various values of the effective number of messenger fields Nmess are possible depending on the choice of the gauge group.
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Topology of gauge groups and gauge equivalence classes of connections.
We then continue to discuss theories with orthogonal and symplectic gauge groups and their dualities.
We start by discussing Chern-Simons matter dualities with unitary gauge groups.
Particularly, we count the numbers of gauge theories with different gauge groups but equal numbers of U 1) factors which are dual to each other.
We clarify the global form of the gauge groups, and we show the level-rank dualities hold generally only between spin topological quantum field theories.
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