A Modified Y-M Action with Three Families of Fermionic Solitons and   Perturbative Confinement
  The dynamics of a four dimensional generally covariant modified SU(N) Yang-Mills action, which depends on the complex structure of spacetime and not its metric, is studied. A general solution of the complex structure integrability conditions is found in the context of the G{2,2) Grassmannian manifold, which admits a global SL(4,C) symmetry group. A convenient definition of the physical energy and momentum permits the study of the vacuum and soliton sectors. The model has a set of conformally SU(2,2) invariant vacua and a set of Poincare invariant vacua. An algebraic integrability condition of the complex structure classifies the solitonic surfaces into three classes (families). The first class (spacetimes with two principal null directions) contains the Kerr-Newman complex structure, which has fermionic (electron-like) properties. That is the correct fermionic gyromagnetic ratio (g=2) and it satisfies the correct electron equations of motion. The conjugate complex structure determines the antisoliton, which has the same mass and opposite charge. The fermionic solitons are differentiated from the complex structure bosonic modes by the periodicity condition on compactified spacetime. The non-periodicity of the found solitonic complex structures is proved. The modification of the Yang-Mills action has an essential consequence to the classical potential. It generates a linear static potential instead of the Coulomb-like (1/r) potential of the ordinary Yang-Mills action. This linear potential implies that for every pure geometric soliton there are N solitonic gauge field excitations, which are perturbatively confined. The present model advocates a solitonic unification scheme without supersymmetry and/or superstrings. 
C. N. Ragiadakos