[en] Description of solutions of Yang-Mills equations with non zero current, in the cases of a current parallel to z-axis or of a solenoidal current with cylindrical symmetry

No abstract available

[en] We compute the principal contribution to the index in the supersymmetric quantum mechanical systems which are obtained by reduction to 0+1 dimensions of N=1, D=4,6,10 super-Yang-Mills theories with gauge group SU(N). The results are: 1/(N²) for D=4,6, sum _{dverticalstrokeN}1/(d²) for D=10. We also discuss the D=3 case. (orig.)

[en] Contemporary topological research in Yang-Mills theory is reviewed, emphasizing the Chern-Simons terms and their relatives. Three applications of the Chern-Simons terms in physical theory are described: to help understanding gauge theories in even dimensional space-time; gauge field dynamics in odd dimensional space-time; and mathematically coherent description of even-dimensional gauge theories with chiral fermions that are apparently inconsistent due to chiral anomalies. Discussion of these applications is preceded by explanation of the mathematical preliminaries and examples in simple quantum mechanical settings. 24 refs

[en] Topological Yang-Mills theory is derived in the framework of Lagrangian BRST cohomology. (orig.)

[en] We show that the superconformal anomalies of super Yang-Mills theory may be correctly calculated using the supersymmetry preserving dimensional regularization by dimensional reduction. (orig.)

[en] The word instanton has been coined by analogy with the word soliton. They both refer to solutions of elliptic non linear field equations with boundary conditions at infinity (of euclidean space time in the first case, euclidean space in the second case) lying on the set of classical vacua in such a way that stable topological properties emerge, susceptible to survive quantum effects, if those are small. Under this assumption, instantons are believed to be relevant to the description of tunnelling effects between classical vacua and signal some characteristics of the vacuum at the quantum level, whereas solitons should be associated with particles, i.e. discrete points in the mass spectrum. In one case the euclidean action is finite, in the other case, the energy is finite. From the mathematical point of view, the geometrical phenomena associated with the existence of solitons have forced physicists to learn rudiments of algebraic topology. The study of euclidean classical Yang Mills fields involves naturally mathematical items falling under the headings: differential geometry (fibre bundles, connections); differential topology (characteristic classes, index theory) and more recently algebraic geometry. These notes are divided as follows: a first section is devoted to a description of the physicist's views; a second section is devoted to the mathematician's vie

[en] A compact Riemannian manifold M is said to be Yang-Mills instable, if for every choice of compact Lie group G and every principle G-bundle P over M, none of the nonflat Yang-Mills connection in P is weakly stable. This paper gives curvature pinching condition for the Yang-Mills instability of hypersurfaces in space form. (author). 3 refs

No abstract available

[en] Using the higher covariant derivative regularization we calculate a two-loop β-function for the N = 1 supersymmetric Yang-Mills theory with the matter superfields, containing the cubic superpotential. It is found that all integrals, defining this function, are integrals of total derivatives.