Abstract

In recent work with Latham Boyle (see arXiv:2110.06258) we point out that, at leading order, 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 highly nontrivial: assuming the gauge group SU3xSU2xU1, they require precisely 3 generations of standard model fermions, each including a right-handed neutrino. Many candidate extensions of the standard model including popular grand unified theories are ruled out by this criterion. The extra scalars have a four-derivative action with potential for ghosts. However, in a careful Euclidean treatment consistent with our recent proposal (see arXiv:2109.06204), we show that a physical state space with only positive energies and norms may be identified. The dimension zero scalars possess a scale-invariant power spectrum in their quantum vacuum, suggesting a new, first-principles explanation of the scalar perturbations in cosmology not requiring inflation. As pointed out earlier, one of the three right handed neutrinos is the simplest yet proposed candidate for the dark matter. This remarkable combination of predictions, spanning a huge range of scales, suggests dimension zero scalars might play a basic role in fundamental physics. If time allows, I will briefly discuss the possible emergence of the Higgs field and the spacetime metric, within this framework.