FUNCTIONAL RENORMALIZATION OF NONCOMMUTATIVE SCALAR FIELD THEORY

In this paper we apply the Functional Renormalization Group Equation (FRGE) to the noncommutative 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 noncommutativity parameter, originally pointed out in R. Gurau and O. J. Rosten, J. High Energy Phys. 0907, 064 (2009), 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 M. Disertori et al., Phys. Lett. B 649, 95 (2007). Finally, we show how the FRGE can be easily used to compute the one-loop beta-functions of the duality covariant model.