A geometrization of the Yang–Mills field, by which an SU(2) gauge theory becomes equivalent to a 3-space geometry – or optical system – is examined. In a first step, ambient space remains Euclidean and current problems on flat space can be looked at from a new point of view. The Wu– Yang ambiguity, for example, appears related to the multiple possible torsions of distinct metric– preserving con...

We present a Lorentz invariant lagrangian formulation for a supersymmetric Yang-Mills vector multiplet in eleven dimensions (11D). The Lorentz symmetry is broken at the field equation level, and therefore the breaking is spontaneous, as in other formulations of supersymmetric theories in 12D or higher dimensions. We introduce a space-like unit vector formed by the gradient of a scalar field, av...

For semisimple groups, possibly multiplied by U~1!’s, the number of Yang-Mills gauge fields is equal to the number of generators of the group. In this paper, it is shown that, for nonsemisimple groups, the number of Yang-Mills fields can be larger. These additional Yang-Mills fields are not irrelevant because they appear in the gauge transformations of the original Yang-Mills fields. Such nonse...

We consider dimensionally reduced three-dimensional supersymmetric Yang– Mills-Chern–Simons theory. Although the N = 1 supersymmetry of this theory does not allow true massive Bogomol'nyi–Prasad–Sommerfield (BPS) states, we find approximate BPS states which have non-zero masses that are almost independent of the Yang–Mills coupling constant and which are a reflection of the massless BPS states ...

We investigate Lie symmetries of general Yang-Mills equations. For this purpose, we first write down the second prolongation of the symmetry generating vector fields, and compute its action on the Yang-Mills equations. Determining equations are then obtained, and solved completely. Provided that Yang-Mills equations are locally solvable, this allows for a complete classification of their Lie sy...

We consider the Yang-Mills flow equations on a reductive coset space G/H and the Yang-Mills equations on the manifold R×G/H . On nonsymmetric coset spaces G/H one can introduce geometric fluxes identified with the torsion of the spin connection. The condition of G-equivariance imposed on the gauge fields reduces the Yang-Mills equations to φ-kink equations on R. Depending on the boundary condit...

We extend the traditional formulation of Gauge Field Theory by incorporating the (non-Abelian) gauge group parameters (traditionally simple spectators) as new dynamical (nonlinear-sigma-model-type) fields. These new fields interact with the usual Yang-Mills fields through a generalized minimal coupling prescription, which resembles the so-called Stueckelberg transformation [1], but for the non-...

We argue that two dimensional classical SU(2) Yang-Mills theory describes the embedding of Riemann surfaces in three dimensional curved manifolds. Specifically , the Yang-Mills field strength tensor computes the Riemannian curvature tensor of the ambient space in a thin neighborhood of the surface. In this sense the two dimensional gauge theory then serves as a source of three dimensional gravi...

We present a mechanism of gauge field localization on a domain wall within the framework of strongly coupled pure Yang-Mills theory.

Yang-Mills gauge field with gauge group SU(2) decomposes into a single charge neutral complex vector, and two spinless charged scalar fields. At high energies these constituents are tightly confined into each other by a compact U(1) interaction, and the Yang-Mills Lagrangian describes the dynamics of asymptotically free massless gauge vectors. But in a low energy and finite density environment ...