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The $\beta$-function in duality-covariant non-commutative $\phi^4$-theory

Authors:	Email author" target="_blank">H?Grosse Email author R?Wulkenhaar

Institution:	(1) Institut für Theoretische Physik, Universität Wien, Boltzmanngasse 5, 1090 Wien, Austria;(2) Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstraße 22-26, 04103 Leipzig, Germany

Abstract:	We compute the one-loop $\beta$ -functions describing the renormalisation of the coupling constant $\lambda$ and the frequency parameter $\Omega$ for the real four-dimensional duality-covariant non-commutative $\phi^4$ -model, which is renormalisable to all orders. The contribution from the one-loop four-point function is reduced by the one-loop wavefunction renormalisation, but the $\beta_\lambda$ -function remains non-negative. Both $\beta_\lambda$ and $\beta_\Omega$ vanish at the one-loop level for the duality-invariant model characterised by $\Omega = 1$ . Moreover, $\beta_\Omega$ also vanishes in the limit $\Omega\to 0$ , which defines the standard non-commutative $\phi^4$ -quantum field theory. Thus, the limit $\Omega\to 0$ exists at least at the one-loop level.Received: 19 March 2004, Published online: 5 May 2004

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