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The dynamics of a four dimensional generally covariant modified SU(N)Yang-Mills action, which depends on the complex structure of spacetime and notits metric, is studied. A general solution of the complex structureintegrability conditions is found in the context of the G{2,2) Grassmannianmanifold, which admits a global SL(4,C) symmetry group. A convenient definitionof the physical energy and momentum permits the study of the vacuum and solitonsectors. The model has a set of conformally SU(2,2) invariant vacua and a setof Poincare invariant vacua. An algebraic integrability condition of thecomplex 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 itsatisfies the correct electron equations of motion. The conjugate complexstructure determines the antisoliton, which has the same mass and oppositecharge. The fermionic solitons are differentiated from the complex structurebosonic modes by the periodicity condition on compactified spacetime. Thenon-periodicity of the found solitonic complex structures is proved. Themodification of the Yang-Mills action has an essential consequence to theclassical potential. It generates a linear static potential instead of theCoulomb-like (1/r) potential of the ordinary Yang-Mills action. This linearpotential implies that for every pure geometric soliton there are N solitonicgauge field excitations, which are perturbatively confined. The present modeladvocates a solitonic unification scheme without supersymmetry and/orsuperstrings.

A Modified Y-M Action with Three Families of Fermionic Solitons and Perturbative Confinement