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

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 $\theta$. 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.

arXiv comment7 pages

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• Noncommutative GUT inspired theories and the UV finiteness of the fermionic four point functions
• Gauge Theories on Deformed Spaces
• Renormalisability of noncommutative GUT inspired field theories with anomaly safe groups
• Particle phenomenology on noncommutative spacetime
• Singlet particles as cold dark matter in noncommutative space-time
• Noncommutative GUT inspired theories with U(1), SU(N) groups and their renormalisability
• TeV Scale Implications of Non Commutative Space time in Laboratory Frame with Polarized Beams
• SO(10) GUTs with large tensor representations on Noncommutative Space-time
• Three dimensional noncommutative bosonization
• Noncommutative N=1 super Yang-Mills, the Seiberg-Witten map and UV divergences
• Higher derivative Chern-Simons extension in the noncommutative QED${}_3$
• Three-dimensional noncommutative Yukawa theory: Induced effective action and propagating modes
• Photon-neutrino interaction in theta-exact covariant noncommutative model: Phenomenology and Quantum properties*