An invitation to Dirac ensembles in (random) Noncommutative Geometry

par Dr Carlos Perez

jeudi 3 févr. 2022, 10:30 → 11:30 Europe/Paris

125 (Braconnier)

In the noncommutative generalization of spin Riemannian geometry, the metric disappears and an abstract Dirac operator undertakes the geometric description. The classical theory shows some appropriateness to accommodate the observed particle spectrum--and gravity. However, the problem of its quantization is open. This talk is an invitation to a path-integral quantization approach of such finite-dimensional geometries named Dirac ensembles (elsewhere: finite random noncommutative geometry or random spectral triples) whose classical theory is determined by Connes-Chamseddine spectral action principle. After a gentle introduction, we:

- reformulate the partition function of such geometries as a
random (multi)matrix problem [1912.13288]

- identify the elements of gauge theory ("Yang-Mills on
a noncommutative space") stated also as a multimatrix model
[2105.01025]

- address, if time allows, the functional renormalization
of the multimatrix models that NCG originates [2007.10914
and 2111.02858].