Abstract
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.
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Communicated by Raimar Wulkenhaar.
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van Suijlekom, W.D. Renormalizability Conditions for Almost-Commutative Manifolds. Ann. Henri Poincaré 15, 985–1011 (2014). https://doi.org/10.1007/s00023-013-0269-1
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DOI: https://doi.org/10.1007/s00023-013-0269-1