The spectral action principle, introduced by Chamseddine and Connes in ’97, produces particle physical models out of spectral triples, be it at the classical level. Mathematically, the spectral action is 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. In this talk, we will expand the spectral action in V and uncover a fascinating cyclic structure. We use this structure to define ribbon graphs and obtain a one-loop quantization of the spectral action. Based on joint work with Walter van Suijlekom.

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