Solution of the self-dual Φ4 QFT-model on four-dimensional Moyal space

Abstract

Abstract Previously the exact solution of the planar sector of the self-dual Φ4-model on 4-dimensional Moyal space was established up to the solution of a Fredholm integral equation. This paper solves, for any coupling constant λ > − 1 π $$ \frac{1}{\uppi} $$ , 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 λπ π $$ \frac{\arcsin \left(\uplambda \uppi \right)}{\uppi} $$ for |λ| 0 avoids the triviality problem of the matricial Φ 4 4 $$ {\varPhi}_4^4 $$ -model. We also establish the power series approximation of the Fredholm solution to all orders in λ. 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.

Keywords

• Integrable Field Theories
• Matrix Models
• Non-Commutative Geometry