String Theory Journal Club

Random noncommutative geometry started in [Barrett-Glaser J. Phys. A 49(2016) 24] and can be seen as an approach to the quantisation of noncommutative geometry. Fuzzy geometries form a class of finite dimensional spectral triples whose spectral action can be computed in terms of noncommutative polynomials. After briefly explaining how, we focus on the algebraic structure of the Functional Renormalisation Group (RG) for multi-matrix models motivated by random noncommutative geometry, which turns out to be described by (a relative of) the free algebra. The motivation is to use this as a tool to find fixed points of the RG-flow, which are candidates for phase-transition. We finish with some progress on how to add matter fields. Based on arXiv:2007.10914. Link: meet.google.com/gbj-tmns-err