# Renormalization and Geometry in the Grosse-Wulkenhaar Model

#### 10.12.2021, 11:00  –  2.22 und online Arbeitsgruppenseminar Analysis

Alexander Hock (Oxford University)

The Grosse-Wulkenhaar model (GW) is a euclidean scalar quantum field theory with quartic interaction on a non-commutative space, more precisely on the Moyal space. The most interesting property of this model is that it can be solved exactly, so we can derive exact expressions for a series of infinitely many Feynman graphs. In four dimensions, this obviously requires renormlization to make the theory UV-finite.
I will show the exact solution of the planar two-point correlation function depending on the dimension, and therefore on the renormalization. For the just-renormalizable four-dimensional case, the exact solution differs significally from two dimensions.
From geometric perspective, some solutions of higher correlation functions will be discussed which have a recursive geometrical interpretation in the sense of Blobbed Topological Recursion. This is generalization of the celebrated universal structure of Topological Recursion invented by Eynard and Orantin. However, the geometric picture is faced with problems in just-renormalizable four-dimensional case due to the necessity of the field renormalization constant $Z$.

For those of you who can and would like to join us, please meet us in the seminar Room 2.22 of the maths institute, where we can follow the talk together.