Functional Renormalization of Noncommutative Scalar Field Theory

Details Functional Renormalization of Noncommutative Scalar Field Theory Functional Renormalization of Noncommutative Scalar Field Theory

2010-06-26

arxiv.org/abs/1006.5145v2

Int.J.Mod.Phys.A26:4009-4051,2011

Physics

High Energy Physics

High Energy Physics - Theory

38 pages, no figures, LaTeX

Scientific paper

10.1142/S0217751X11054048

In this paper we apply the Functional Renormalization Group Equation (FRGE) to the non-commutative scalar field theory proposed by Grosse and Wulkenhaar. We derive the flow equation in the matrix representation and discuss the theory space for the self-dual model. The features introduced by the external dimensionful scale provided by the non-commutativity parameter, originally pointed out in \cite{Gurau:2009ni}, are discussed in the FRGE context. Using a technical assumption, but without resorting to any truncation, it is then shown that the theory is asymptotically safe for suitably small values of the $\phi^4$ coupling, recovering the result of \cite{disertori:2007}. Finally, we show how the FRGE can be easily used to compute the one loop beta-functions of the duality covariant model.

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