Solution of the self-dual φ4 QFT-model on four-dimensional Moyal space

Previously the exact solution of the planar sector of the self-dual phi(4)-model on 4-dimensional Moyal space was established up to the solution of a Fredholm integral equation. This paper solves, for any coupling constant lambda > -1 pi, the Fredholm equation in terms of a hypergeometric function and thus completes the construction of the planar sector of the model. We prove that the interacting model has spectral dimension 4 - 2 arcsin for |lambda| <1 pi. It is this dimension drop which for lambda > 0 avoids the triviality problem of the matricial phi 44-model. We also establish the power series approximation of the Fredholm solution to all orders in lambda. The appearing functions are hyperlogarithms defined by iterated integrals, here of alternating letters 0 and -1. We identify the renormalisation parameter which gives the same normalisation as the ribbon graph expansion.