# Algebraic Structures in Perturbative Quantum Field Theory

16-20 November 2020
IHES
Europe/Paris timezone

## Solution of $\phi^4_4$ on the Moyal Space

19 Nov 2020, 15:15
30m
Marilyn and James Simons Conference Center (IHES)

### Marilyn and James Simons Conference Center

#### IHES

35 route de Chartres, F-91440 Bures-sur-Yvette, France

### Speaker

Dr Alexander Hock (Westfälische Wilhelms-Universität Münster)

### Description

We show the exact solution of the self-dual $\phi^4$-model on the 4-dimensional Moyal space. Using the results explained in Raimar's talk, an implicitly defined function converges to a Fredholm integral, which is solved, for any coupling constant $\lambda>-\frac{1}{\pi}$, in terms of a hypergeometric function. We prove that the interacting model has spectral dimension $4-2\frac{\arcsin(\lambda\pi)}{\pi}$ for $|\lambda|<\frac{1}{\pi}$. It is this dimension drop which for $\lambda>0$ avoids the triviality problem of the $\phi^4_4$ model on the Moyal space.