Hadronic Sector in the 4-d Pseudo-Conformal Field Theory.
The pseudo-conformal field theory (PCFT) is a 4-d action, which depends on the lorentzian Cauchy-Riemann (LCR) structure. Like the 2-d Polyakov action, it does not depend on the metric tensor. But the invariance under the pseudo-conformal transformations (in the terminology of E. Cartan and Tanaka) imposes in the action the existence of a gauge field instead of the scalar field of the Polyakov action. The tetrad of the LCR-structure defines a class of metrics and a corresponding class of self dual 2-forms. I prove that the inverse is also valid. Einstein has showed that the equations of motion of the black-hole essential singularities is a consequence of the regularity of the metric tensor. Hence its equivalence with the LCR-structure implies that these equations assure the regularity of the LCR-structures. This permit us to determine the multisolitons of the PCFT. After the expansion of the action around the static LCR-structure soliton, the quadratic part of the Yang-Mills-like term implies a linear partial differential equation (PDE). I solve this PDE using the Teukolsky method of solution of the electromagnetic field in the background of the Kerr black hole. The angular and radial ODEs are different to the corresponding Teukolsky master equations, permitting the possible identification of the quark as a soliton bound state of the static LCR-structure and the gluon. These two results opens up the possibility of the numerical computations of the standard model parameters and the hadron form factors, permitting the experimental check of PCFT.
Publisher URL: http://arxiv.org/abs/1811.04428