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Using the recently proposed nonlinear gauge conditionwe show the area law behavior of the Wilson loop and the linear dependence of the instantaneous gluon propagator. The field configurations responsible for confinement are those in the nonlinear sector of the gauge-fixing condition (the linear sector being the Coulomb gauge). The nonlinear sector is actually composed of "Gribov horizons" on the parallel surfaces ∂ · A a = f a = 0. In this sector, the gauge field A a µ can be expressed in terms of f a and a new vector field t a µ . The effective dynamics of f a suggests nonperturbative effects. This was confirmed by showing that all spherically symmetric (in 4-D Euclidean) f a (x) are classical solutions and averaging these solutions using a Gaussian distribution (thereby treating these fields as random) lead to confinement. In essence the confinement mechanism is not quantum mechanical in nature but simply a statistical treatment of classical spherically symmetric fields on the "horizons" of ∂ · A a = f a (x) surfaces.

The Parisi-Sourlas mechanism is exhibited in pure Yang-Mills theory. Using the new scalar degrees of freedom derived from the non-linear gauge condition, we show that the non-perturbative sector of Yang-Mills theory is equivalent to a 4D O(1, 3) sigma model in a random field. We then show that the leading term of this equivalent theory is invariant under supersymmetry transformations where x 2 + θθ is unchanged. This leads to dimensional reduction proving the equivalence of the non-perturbative sector of Yang-Mills theory to a 2D O(1, 3) sigma model.

We show a different modification of Poincare algebra that also preserves the Lorentz algebra. The change begins with how boosts affect space-time in a way similar to how boosts affect the momenta in kappa Poincare algebra, thus the name dual kappa Poincare algebra. Since by construction the new space-time commutes, it follows that the momenta co-commute. Proposing a space-time coalgebra that is similar to the momentum co-product in the bicrossproduct basis of kappa Poincare algebra, the phase space algebra is derived using the Heisenberg double construction. The phase space variables of the dual kappa Poincare algebra are then related to SR phase space variables.From these relations, we complete the dual kappa Poincare algebra by deriving the action of rotations and boosts on the momenta. PACS numbers: