Cancelling the vacuum energy and Weyl anomaly in the standard model with dimension zero scalars

In recent work with Latham Boyle, we observe that the vacuum energy and the Weyl anomaly in the gauge/fermion part of the standard model are cancelled by 36 Weyl-invariant, dimension zero scalars. The cancellations are nontrivial: assuming the standard model gauge group SU3xSU2xU1, they imply precisely 3 generations of standard model fermions (each including a right handed neutrino). The extra scalars have a four derivative action with potential for ghosts. However, in a careful Euclidean treatment consistent with our recent proposal, we show that a physical state space with only positive energies and norms may be identified. The dimension zero scalars have a scale-invariant power spectrum in their quantum vacuum, suggesting a new, first-principles explanation of the scalar perturbations in cosmology without inflation. This remarkable set of predictions, over a vast span of scales, suggests dimension zero scalars may play a basic role in fundamental physics. I will discuss the possible emergence of the Higgs field and the spacetime metric in this framework.  

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