paper

Noncommutative N=1 super Yang-Mills, the Seiberg-Witten map and UV divergences

arXiv:0907.2437 · doi:10.1088/1126-6708/2009/11/092

Abstract

Classically, the dual under the Seiberg-Witten map of noncommutative U(N), {\cal N}=1 super Yang-Mills theory is a field theory with ordinary gauge symmetry whose fields carry, however, a θ-deformed nonlinear realisation of the {\cal N}=1 supersymmetry algebra in four dimensions. For the latter theory we work out at one-loop and first order in the noncommutative parameter matrix θ^{μν} the UV divergent part of its effective action in the background-field gauge, and, for N>=2, we show that for finite values of N the gauge sector fails to be renormalisable; however, in the large N limit the full theory is renormalisable, in keeping with the expectations raised by the quantum behaviour of the theory's noncommutative classical dual. We also obtain --for N>=3, the case with N=2 being trivial-- the UV divergent part of the effective action of the SU(N) noncommutative theory in the enveloping-algebra formalism that is obtained from the previous ordinary U(N) theory by removing the U(1) degrees of freedom. This noncommutative SU(N) theory is also renormalisable.

33 pages, 4 figures. Version 2: Unnecessary files removed. Version 3: New types of field redefinitions were considered, which make the large N U(N) and the SU(N) theories renormalisable. The conclusions for U(N) with finite N remain unchanged. Version 4: Corrected mistyped equations, minor revisions

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