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Noncommutative Induced Gauge Theory

Axel de Goursac·Jean-Christophe Wallet·Raimar Wulkenhaar
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Abstract

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 $ϕ^4$-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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Axel de Goursac, Jean-Christophe Wallet, Raimar Wulkenhaar. 2007-03-09. Noncommutative Induced Gauge Theory. https://doi.org/10.1140/epjc%2Fs10052-007-0335-2

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