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.
Highlights
SEMINAR ZAVODA ZA TEORIJSKU FIZIKU (Zajednicki seminari Zavoda za teorijsku fiziku, Zavoda za eksperimentalnu fiziku i Zavoda za teorijsku fiziku PMF-a)
The reasons behind the observed renormalisability of the matter contributions to the gauge sector of the effective action, which holds independently of the matter content, will be explained. This will be done by considering a noncommutative gauge theory defined for an arbitrary semisimple gauge group, with Dirac fermionas or complex scalars in an arbitrary representation of the group, and computing the one-loop UV divergent matter contributions to the gauge field effective action to all orders in the noncommutative parameters θ
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
Summary
SEMINAR ZAVODA ZA TEORIJSKU FIZIKU (Zajednicki seminari Zavoda za teorijsku fiziku, Zavoda za eksperimentalnu fiziku i Zavoda za teorijsku fiziku PMF-a). (Zajednicki seminari Zavoda za teorijsku fiziku, Zavoda za eksperimentalnu fiziku i Zavoda za teorijsku fiziku PMF-a)
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