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

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Ragiadakos, C. N.

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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 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.

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High Energy Physics - Theory, General Relativity and Quantum Cosmology