A Caltech Library Service

Gravity and the standard model with neutrino mixing

Chamseddine, Ali H. and Connes, Alain and Marcolli, Matilde (2007) Gravity and the standard model with neutrino mixing. Advances in Theoretical and Mathematical Physics, 11 (6). pp. 991-1089. ISSN 1095-0761. doi:10.4310/ATMP.2007.v11.n6.a3.

PDF - Published Version
See Usage Policy.

[img] PDF - Submitted Version
See Usage Policy.


Use this Persistent URL to link to this item:


We present an effective unified theory based on noncommutative geometry for the standard model with neutrino mixing, minimally coupled to gravity. The unification is based on the symplectic unitary group in Hilbert space and on the spectral action. It yields all the detailed structure of the standard model with several predictions at unification scale. Besides the familiar predictions for the gauge couplings as for GUT theories, it predicts the Higgs scattering parameter and the sum of the squares of Yukawa couplings. From these relations, one can extract predictions at low energy, giving in particular a Higgs mass around 170 GeV and a top mass compatible with present experimental value. The geometric picture that emerges is that space-time is the product of an ordinary spin manifold (for which the theory would deliver Einstein gravity) by a finite noncommutative geometry F. The discrete space F is of KO-dimension 6 modulo 8 and of metric dimension 0, and accounts for all the intricacies of the standard model with its spontaneous symmetry breaking Higgs sector.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Additional Information:© 2007 International Press. It is a pleasure to acknowledge the independent preprint by John Barrett [4] with a solution of the fermion doubling problem. The first author is supported by NSF Grant Phys-0601213. The second author thanks G. Landi and T. Schucker, the third author thanks Laura Reina and Don Zagier for useful conversations. We thank the Newton Institute where part of this work was done.
Funding AgencyGrant Number
Subject Keywords:noncommutative geometry; renormalization-group; spectral action; gauge-theories; unification; relativity
Issue or Number:6
Record Number:CaltechAUTHORS:CHAatmp07
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13602
Deposited By: Tony Diaz
Deposited On:11 May 2009 18:50
Last Modified:08 Nov 2021 22:39

Repository Staff Only: item control page