Conformal Symmetry, SM and Gravity

Abstract

This paper is a bottom-up attempt to incorporate the standard model and general relativity in a unique quantum field theory. In particular, the tentative model presented here is free of chiral gauge and gravitational anomalies that appear in the divergence of currents and in the divergence and trace of the energy–momentum tensor when SM matter couples to gravity. The fermion spectrum is composed of two multiplets: the SM (left) multiplet and a mirror copy (right) with opposite handedness. The right multiplet is interpreted as describing the dark matter world. The natural symmetry of the theory is enlarged to incorporate Weyl invariance by introducing one or more dilaton fields. After the cosmological and theoretical motivations, the necessary formalism is introduced for algebraic renormalization: gauge fixings, ghosts, propagators, vertices and their interplay in guaranteeing the conditions for convergence of the subtracted amplitudes according to the BPHZL scheme, the Slavnov–Taylor identity, and the relevant enlarged BRST symmetry. The corresponding (conformal) cohomology is analyzed and found to be trivial: there are no non-trivial even trace anomalies in theories with dilatons, but there are plenty of trivial ones that require corresponding counterterms in the effective action. It is shown that such counterterms can play an important role in freeing the theory from unphysical particles.