We consider the L 2-gradient ow associated with the Yang-Mills functional, the so-called Yang-Mills heat ow. In the setting of a trivial principal SO(n)-bundle over R n in dimension n greater than 4, we show blow-up in nite time for a class of SO(n)-equivariant initial connections.

The effective action of N=2 Yang-Mills theory with adjoint matter is shown to be governed by an integrable spin model with spectral parameter on an elliptic curve. We sketch a route to deriving this effective dynamics from the underlying Yang-Mills theory. Natural generalizations of this structure to all N=2 models, and to string theory, are suggested.

We study the dispersion relation for scalar excitations in supersymmetric, noncommutative theories at finite temperature. In N =4 Yang-Mills the low momenta modes have superluminous group velocity. In the massless Wess-Zumino model the minimum of the dispersion relation is at non zero momentum for temperatures above T0 ≈ (gθ) 1 2 . We briefly comment on N =2 Yang-Mills at finite density.

A solution to Slavnov–Taylor identities in a general four dimensional N=1 supersymmetric Yang-Mills theory containing arbitrary matter superfields is proposed. The solution proposed appears just a simple generalization of an analogous solution in the pure supersymmetric Yang-Mills theory.

We study a stationary, spherically symmetric system of (2j + 1) massive Dirac particles, each having angular momentum j, j = 1, 2, . . ., in a classical gravitational and SU(2) Yang-Mills field. We show that for any black hole solution of the associated Einstein-Dirac-Yang/Mills equations, the spinors must vanish identically outside of the event horizon.

Two classes of observables defined on the phase space of a particle are quantized, and the effects of the Yang-Mills field are discussed in the context of geometric quantization. PACS: 03.65.Bz, 02.40.Vh Short title: Particle in background Yang-Mills field.

We present new exact solutions of the Einstein-Yang-Mills system. The solutions are described by a null Yang-Mills field in a Kundt spacetime. They generalize a previously known solution for a metric of pp wave type. The solutions are formally of Petrov type III.

We consider the Super Yang–Mills/spin system map to construct the SU(2) spin bit model at the level of two loops in Yang–Mills perturbation theory. The model describes a spin system with chaining interaction. In the large N limit the model is shown to be reduced to the two loop planar integrable spin chain.

Anti-normal quantization of relativistic Yang-Mills fields with a compact semisimple gauge group mathematically produces an infinite discrete energymass spectrum of Z′ gauge bosons. In particular, quantum Yang-Mills theory existence and mass gap problem is solved. To I. M. Gelfand with gratitude.

The explicit form of non-Abelian noncommutative supersymmetric (SUSY) chiral anomaly is calculated, the Wess–Zumino consistency condition is verified and the correspondence of the Yang–Mills sector to the previously obtained results is shown. We generalize the Seiberg–Witten map to the case of N=1 SUSY Yang–Mills theory and calculations up to the second order in the noncommutativity parameter a...