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

TL;DR

This paper develops a 4-dimensional pseudo-conformal field theory based on Lorentzian Cauchy-Riemann structures, unifying gravity, electroweak, and strong interactions with novel solitonic solutions and particle identifications.

Contribution

It introduces a renormalizable 4D action with metric independence, linking LCR-structures to fundamental particles and interactions, extending Polyakov's 2D approach to four dimensions.

Findings

Identifies LCR-structures with electrons and neutrinos.

Derives an effective leptonic standard model action.

Explains quark-lepton correspondence via solitonic gauge fields.

Abstract

The characteristic property of the 2-dimensional Polyakov action is its independence on the metric tensor, without being topological. A renormalizable 4-dimensional action is found satisfying this fundamental property. 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 implies the Kerr-Newman manifold with g=2 gyromagnetic ratio and it is identified with the electron. The stationary (reducible) LCR-structure is identified with the neutrino. The antiparticles have conjugate LCR-structures. The Hawking-Penrose singularity theorems are bypassed in the electron LCR-manifold. 4) The LCR-tetrad defines Einstein's metric and the U(2) electroweak connection. 5) An effective leptonic standard model action is derived using the Bogoliubov-Scharf recursive procedure. 6) The three generations of flavors are implied by the limited number (for curved spacetime) 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. 8) The derivation of a proper geometric SU(3) Cartan connection opens up the possibility to achieve Einstein's goal to derive all interactions from the pure geometric LCR-structure.