Functional Renormalization of Noncommutative Scalar Field Theory
Abstract
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 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 φ4 coupling, recovering the result of disertori:2007. Finally, we show how the FRGE can be easily used to compute the one loop beta-functions of the duality covariant model.