Noncommutative induced gauge theory |
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Authors: | A de Goursac J-C Wallet R Wulkenhaar |
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Institution: | 1. Laboratoire de Physique Théorique, Bat. 210, Université Paris XI, 91405, Orsay Cedex, France 2. Mathematisches Institut der Westf?lischen Wilhelms-Universit?t, Einsteinstra?e 62, 48149, Münster, Germany
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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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Keywords: | |
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