Noncommutative induced gauge theory

Marcillaud de Goursac, Axel;Wallet, Jean-Christophe;Wulkenhaar, Raimar
(2007) European Physical Journal C. Particles and Fields — Vol. 51, p. 977-987 (2007)

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  • Marcillaud de Goursac, AxelUCLouvain
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  • Wallet, Jean-ChristopheUniversité Paris-Sud 11
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  • Wulkenhaar, RaimarUniversity of Münster
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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 ϕ4-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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Marcillaud de Goursac, A., Wallet, J.-C., & Wulkenhaar, R. (2007). Noncommutative induced gauge theory. European Physical Journal C. Particles and Fields, 51, 977-987. https://doi.org/10.1140/epjc/s10052-007-0335-2 (Original work published 2007)