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arXiv · 0706.4052

Renormalisability of the matter determinants in noncommutative gauge theory in the enveloping-algebra formalism

C. P. Martin·C. Tamarit
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Abstract

We consider noncommutative gauge theory defined by means of Seiberg-Witten maps for an arbitrary semisimple gauge group. We compute the one-loop UV divergent matter contributions to the gauge field effective action to all orders in the noncommutative parameters $θ$. We do this for Dirac fermions and complex scalars carrying arbitrary representations of the gauge group. We use path-integral methods in the framework of dimensional regularisation and consider arbitrary invertible Seiberg-Witten maps that are linear in the matter fields. Surprisingly, it turns out that the UV divergent parts of the matter contributions are proportional to the noncommutative Yang-Mills action where traces are taken over the representation of the matter fields; this result supports the need to include such traces in the classical action of the gauge sector of the noncommutative theory.

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C. P. Martin, C. Tamarit. 2007-06-27. Renormalisability of the matter determinants in noncommutative gauge theory in the enveloping-algebra formalism. https://doi.org/10.1016/j.physletb.2007.08.033

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