Scale Invariance in the Spectral Action

Details Scale Invariance in the Spectral Action Scale Invariance in the Spectral Action

2005-12-14

arxiv.org/abs/hep-th/0512169v3

J.Math.Phys.47:063504,2006

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, spectral function defined, one reference added. Form to be published in Journal Mathematical Physics

Scientific paper

10.1063/1.2196748

The arbitrary mass scale in the spectral action for the Dirac operator in the spectral action is made dynamical by introducing a dilaton field. We evaluate all the low-energy terms in the spectral action and determine the dilaton couplings. These results are applied to the spectral action of the noncommutative space defined by the standard model. We show that the effective action for all matter couplings is scale invariant, except for the dilaton kinetic term and Einstein-Hilbert term. The resulting action is almost identical to the one proposed for making the standard model scale invariant as well as the model for extended inflation and has the same low-energy limit as the Randall-Sundrum model. Remarkably, all desirable features with correct signs for the relevant terms are obtained uniquely and without any fine tuning.

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