We discuss an analytic approach towards the solution of pure Yang-Mills theory in 3+1 dimensional spacetime. The approach is based on the use of local gauge invariant variables in the Schrödinger representation and the large N , planar limit. In particular, within this approach we point out unexpected parallels between pure Yang-Mills theory in 2+1 and 3+1 dimensions. The most important paralle...

A center vortex model for the infrared sector of SU(4) Yang-Mills theory is constructed such as to reproduce both the ratio between the zero-temperature quark and diquark string tensions known from lattice Yang-Mills theory, as well as the properties of the deconfinement transition. On this basis, the temperature dependence of the spatial quark and diquark string tensions is predicted. Though s...

Quantum Yang–Mills theory can be rewritten in terms of gauge-invariant variables: it has the form of BF gravity, with an additional ‘æther’ term. The BF gravity based on the gauge group SU(N) is actually a theory of high spin fields (up to J = N) with high local symmetry mixing up fields with different spins – like in supergravity but without fermions. At N → ∞ one gets a theory with an infinit...

We find solutions of the Yang-Mills field equations with gauge group SU(2) in 4k dimensions which have the interpretation of four-dimensional instantons at angles. These configurations satisfy a BPS-like condition which arises in the context of two-dimensional (4,0)-supersymmetric sigma models. Moreover we show that these solutions are examples of Hermitian-Einstein connections on E. In the pas...

Local effective action is derived to describe Regge asymptotic of Yang–Mills theories. Local symmetries of the effective action originating from the gauge symmetry of the underlying Yang–Mills theory are studied. Multicomponent effective action is introduced to express the symmetry transformations as field transformations. The algebra of these symmetries is decomposed onto a semi-direct sum of ...

We present a kinetic theory for swarming systems of interacting, self-propelled discrete particles. Starting from the Liouville equation for the many-body problem we derive a kinetic equation for the single particle probability distribution function and the related macroscopic hydrodynamic equations. General solutions include flocks of constant density and fixed velocity and other non-trivial m...

We present a first numerical evidence for the existence of a novel magnetic condensate proposed recently by one of the authors in SU(2) Yang-Mills theory. In our framework, the spontaneously generated color magnetic field identified with the Savvidy vacuum has the microscopic origin and is a consequence of the intrinsic dynamics of the Yang-Mills theory. It strongly suggests the Nielsen– Olesen...

We provide an action for self-dual Yang-Mills theory which is a simple truncation of the usual Yang-Mills action. Only vertices that violate helicity conservation maximally are included. One-loop amplitudes in the self-dual theory then follow as a subset of the Yang-Mills ones. In light-cone gauges this action is almost identical to previously proposed actions, but in this formulation the vanis...

In enlarging the field content of pure Yang-Mills theory to a cutoff dependent matrix valued complex scalar field, we construct a vectorial operator, which is by definition invariant with respect to the gauge transformation of the Yang-Mills field and with respect to a Stueckelberg type gauge transformation of the scalar field. This invariant operator converges to the original Yang-Mills field ...

Some time ago, Svetitsky and Yaffe have argued that — if the de-confinement phase transition of a (d + 1)-dimensional Yang-Mills theory with gauge group G is second order — it should be in the universal-ity class of a d-dimensional spin model symmetric under the center of G. For d = 3 these arguments have been confirmed numerically only in the SU(2) case with center Z Z(2), simply because all S...