Some remarks on Feynman rules for non-commutative gauge theories based on groupsG$\not=$U(N)

Abstract

We study for subgroups G ⊆ U(N) partial summations of the θ-expanded perturbation theory. On diagrammatic level a summation procedure is established, which in the U(N) case delivers the full star-product induced rules. Thereby we uncover a cancellation mechanism between certain diagrams, which is crucial in the U(N) case, but set out of work for G ⊂ U(N). In addition, an explicit proof is given that for G ⊂ U(N), G = U(M), M < N there is no partial summation of the θ-expanded rules resulting in new Feynman rules using the U(N) star-product vertices and besides suitable modified propagators at most a f inite number of additional building blocks. Finally, we show that certain SO(N) Feynman rules conjectured in the literature cannot be derived from the enveloping algebra approach.

Seiberg-Witten maps and noncommutative Yang-Mills theories for arbitrary gauge groups

“…5 For our purposes it is sufficient to do this in terms of the variables of the commutative theory (for simplicity we shall restrict the discussion to models without matter fields). Given two Seiberg-Witten maps determined respectively by:…”

“…The purpose of this work is to elaborate on the construction of noncommutative Yang-Mills theories for arbitrary gauge groups proposed in [1,2] (see also [3,4,5] for related work). The idea in [1,2] is to use a Seiberg-Witten map for building gauge fields and gauge parameters of the noncommutative theory from Lie algebra valued gauge fields and gauge parameters of a commutative gauge theory.…”