From 2-d Polyakov Action to the 4-d Pseudo-Conformal Field Theory

Abstract

The characteristic property of the 2-d Polyakov action is its independence on the metric tensor, without being topological. A renormalizable 4-d action is found with this fundamental property. It is invariant under the pseudo-conformal transformations and it contains a gauge field instead of the scalar field (the embedding function to the ambient 26-d spacetime) of the string action. The fundamental quantity of this pseudo-conformal field theory (PCFT) is the lorentzian Cauchy-Riemann (LCR) structure. This action describes all current phenomenology: 1) The Poincar\'e group is determined. 2) Stable solitonic LCR-tetrads are found, which belong to representations of the Poincar\'e group and they are determined by the irreducible and reducible algebraic quadratic surfaces of CP3. 3) The static (irreducible) LCR-structure is identified with the electron and the stationary (reducible) one is identified with the neutrino. The antiparticles have conjugate LCR-structures. 4) The LCR-tetrad defines Einstein's metric and the electromagnetic tensor for all the solitons. 5) An effective leptonic standard model action is derived using the Bogoliubov recursive procedure. 6) The three generations of flavors are implied by the limited number of permitted algebraic surfaces of CP3. 7) For every LCR-structure there exists a solitonic distributional gauge field configuration, identified with the corresponding quark, which explains the lepton-quark correspondence. It is explicitly computed for the static LCR-structure and a quark confinement mechanism is proposed