Anomalies, Dimensional Regularization and Noncommutative Geometry: Unfinished Draft

In this paper we show that the Breitenlohner-Maison prescription for treating the presence of chiral symmetry in Dimensional Regularization fits remarkably well with the framework of noncommutative geometry. In fact, it corresponds to taking the cup product of spectral triples, with a specific spectral triple Xz whose dimension spectrum is a single complex number z. We give a realization of Xz using the space of Q-lattices. We introduce a formalism of “evanescent gauge potentials” and relate the computation of anomalous graphs in dimension 2 and 4 to local index cocycles. We draw a dictionary of analogies between evanescent gauge potentials and vanishing cycles in algebraic geometry.