On random multimatrix models motivated by noncommutative geometry

par Carlos I. Perez-Sanchez (Universität Heidelberg)

mercredi 24 nov. 2021, 14:00 → 15:00 Europe/Paris

https://greenlight.lal.cloud.math.cnrs.fr/b/fab-49u-gkt

After arXiv:1912.13288, 2007.10914 and 2105.01025.

In high energy physics, one achievement of noncommutative geometry (NCG) is the possibility to actually derive the observed particle spectrum (the Standard Model) from a simple input. This noncommutative geometrical description of matter works only at a classical level (and for the rest, the theory is 'patched' with ordinary quantum field theory methods). The main topic of this talk is a path-integral quantization approach that leads to the concept of 'random noncommutative geometry', i.e. ensembles of Dirac operators, the finite approximations of which can be restated as random multi-matrix ensembles with wildly non-factorizable measures and multi-trace interactions. After a friendly introduction to these topics, I will present a Dirac ensemble which can be identified with Yang-Mills-Higgs matrix theory. If time allows, I will discuss the functional renormalization of the type multimatrix models that NCG motivates.