(Special talk): Non-perturbative RG flows for Higgs-like fields
Prof. Andre Leclair (Cornell University)

We consider 2 coupled Higgs doublets which transform in the usual way under SU(2)⊗U(1). By constructing marginal operators which satisfy an operator product expansion based on the SU(2) Lie algebra, we can obtain a rich pattern of renormalization group (RG) flows which includes lines
of fixed points and more interestingly, cyclic RG flows which are unavoidable in this model. The hamiltonian is pseudo-hermitian, $H^\dagger = K H K$ with $K$ unitary satisfying $K^2 = 1$, thus the model is non-unitary. The hamiltonian still has real eigenvalues, but the non-unitarity is manifested in negative norm states. One can use the operator K to define projection operators onto positive norm states, and in this sub-Hilbert space the time evolution is unitary with positive probabilities. Upon spontaneous symmetry breaking, the Higgs fields have an infinite number of vacuum expectation
values $v_n$ which satisfy “Russian Doll” scaling $v_n \sim e^{2n \lambda}$ where n= 1,2,3,...and $\lambda$ is the period of one RG cycle which is an RG invariant. We speculate that this Russian Doll RG flow can perhaps resolve the so-called hierarchy problem and may shed light on the origin of “families” in the Standard Model of particle physics