2011/12/20 by van Suijlekom, Walter D.
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1112.4690
We formulate conditions under which the asymptotically expanded spectral action on an almost commutative manifold is renormalizable as a higher-derivative gauge theory. These conditions are of graph theoretical nature, involving the Krajewski diagrams that classify such manifolds. This generalizes our previous result on (super)renormalizability of the asymptotically expanded Yang-Mills spectral action to a more general class of particle physics models that can be described geometrically in terms of a noncommutative space. In particular, it shows that the asymptotically expanded spectral action which at lowest order gives the Standard Model of elementary particles is renormalizable.