  The pseudo-conformal field theory (PCFT) is a 4-d action, which depends on
the lorentzian Cauchy-Riemann (LCR) structure. Like the 2-d linearized string
action, it does not depend on the metric tensor. But the invariance under the
pseudo-conformal transformations imposes in the action the existence of a gauge
field instead of the scalar field of the string action. The tetrad of the
LCR-structure defines a class of metrics and a corresponding class of self dual
2-forms. Soliton and multisoliton point of view of PCFT is described and
related to the Einstein derivation of the equations of motion. 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 for the solution of the
electromagnetic field in the background of the Kerr black hole. The angular and
radial ODEs are different from the corresponding Teukolsky master equations.
The exact gauge field PDEs are also solved, solved, using the fundamental
property of LCR-structure coordinates. The found solutions have colored
sources, which could be identified with the quarks.
