One-Loop Renormalizability of the Spectral Action Using Cyclic Cocycles

Explore the one-loop renormalizability of the spectral action using cyclic cocycles in this 44-minute conference talk from the Workshop on "Non-commutative Geometry meets Topological Recursion" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the spectral action principle, introduced by Chamseddine and Connes in 1997, which successfully reproduces the Standard Model Lagrangian including the Higgs boson, massive neutrinos, and gravity. Examine the mathematical representation of the spectral action as Trace(f(D+V)), where f is a test function, D is the Dirac operator of the spectral triple, and V is a bounded perturbation. Discover the fascinating cyclic structure revealed by expanding the spectral action in V, and learn how this structure is used to define ribbon graphs and obtain one-loop renormalizability of the spectral action. Gain insights into the open problem at higher-loop levels and explore connections with work done on the Grosse-Wulkenhaar model. This talk, presented by Teun van Nuland and based on joint work with Walter van Suijlekom, offers a deep dive into advanced mathematical concepts at the intersection of non-commutative geometry and particle physics.