Noncommutative Induced Gauge Theory

Details Noncommutative Induced Gauge Theory Noncommutative Induced Gauge Theory

2007-03-08

arxiv.org/abs/hep-th/0703075v2

Eur.Phys.J.C51:977-987,2007

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, 6 figures

Scientific paper

10.1140/epjc/s10052-007-0335-2

We consider an external gauge potential minimally coupled to a renormalisable scalar theory on 4-dimensional Moyal space and compute in position space the one-loop Yang-Mills-type effective theory generated from the integration over the scalar field. We find that the gauge invariant effective action involves, beyond the expected noncommutative version of the pure Yang-Mills action, additional terms that may be interpreted as the gauge theory counterpart of the harmonic oscillator term, which for the noncommutative $\phi^4$-theory on Moyal space ensures renormalisability. The expression of a possible candidate for a renormalisable action for a gauge theory defined on Moyal space is conjectured and discussed.

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