Renormalizability conditions for almost-commutative geometries

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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7 pages. To appear in Phys. Lett. B

Scientific paper

We formulate conditions for almost-commutative (spacetime) manifolds under which the asymptotically expanded spectral action is renormalizable. These conditions are of a graph-theoretical nature, involving the Krajewski diagrams that classify such geometries. This applies in particular to the Standard Model of particle physics, giving a graph-theoretical argument for its renormalizability. A promising potential application is in the selection of physical (renormalizable) field theories described by almost-commutative geometries, thereby going beyond the Standard Model.

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