Renormalizability conditions for almost-commutative geometries
arXiv:1204.4070 · doi:10.1016/j.physletb.2012.04.040
Abstract
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.
7 pages. To appear in Phys. Lett. B
References in corpus (8)
- A Lorentzian version of the non-commutative geometry of the standard model of particle physics
- On a Classification of Irreducible Almost-Commutative Geometries IV
- Renormalization of the asymptotically expanded Yang-Mills spectral action
- Almost-Commutative Geometries Beyond the Standard Model II: New Colours
- Almost-Commutative Geometries Beyond the Standard Model III: Vector Doublets
- Renormalization of the spectral action for the Yang-Mills system
- On the noncommutative standard model
- Renormalizability conditions for almost commutative manifolds