Locally Scale Invariant Chern-Simons Actions in 3+1 Dimensions and Their Emergence From 4+2 Dimensional 2T-Physics

Abstract

The traditional Chern-Simons (CS) terms in 3+1 dimensions that modify General Relativity (GR), Quantum Chromodynamics (QCD), and Quantum Electrodynamics (QED), typically lack scale invariance. However, a locally scale invariant and geodesically complete framework for the Standard Model (SM) coupled to GR was previously constructed by employing a tailored form of local scale (Weyl) symmetry. This refined SM+GR model closely resembles the conventional SM in subatomic realms where gravitational effects are negligible. Nevertheless, it offers an intriguing prediction: the emergence of new physics beyond the traditional SM and GR near spacetime singularities, characterized by intense gravity and substantial deviations in the Higgs field. In this study, we expand upon the enhanced SM+GR by incorporating Weyl invariant CS terms for gravity, QCD, and QED in 3+1 dimensions, thereby integrating CS contributions within the locally scale-invariant and geodesically complete paradigm. Additionally, we establish a holographic correspondence between the new CS terms in 3+1 dimensions and novel 4+2 dimensional CS-type actions within 2T-physics. We demonstrate that the Weyl transformation in 3+1 dimensions arises from 4+2 general coordinate transformations, which unify the hidden extra 1+1 large (not curled up) dimensions with the evident 3+1 dimensions. By leveraging the newfound local conformal symmetry, the augmented and geodesically complete SM+GR+CS introduces innovative tools and perspectives for exploring classical field theory aspects of black hole and cosmological singularities in 3+1 dimensions, while the 4+2 dimensional connection unveils deeper facets of spacetime.