ar X iv : m at h - ph / 0 10 70 27 v 1 2 7 Ju l 2 00 1 Yang – Mills fields as optical media

ar X iv : 0 70 7 . 40 06 v 1 [ he p - th ] 2 6 Ju l 2 00 7 Two - loop Gell - Mann – Low function of N = 1 supersymmetric

Two-loop Gell-Mann–Low function of N=1 supersymmetric Yang-Mills theory, regularized by higher covariant derivatives. Abstract Two-loop Gell-Mann–Low function is calculated for N=1 supersymmetric Yang– Mills theory, regularized by higher covariant derivatives. The integrals, which define it, are shown to be reduced to total derivatives and can be easily calculated analytically .

ar X iv : m at h - ph / 0 60 70 40 v 1 2 0 Ju l 2 00 6 Invariant Form of BK - factorization and its Applications

ar X iv : 0 70 7 . 33 03 v 1 [ m at h . O A ] 2 3 Ju l 2 00 7 OPERATOR - VALUED FRAMES

ar X iv : h ep - l at / 9 70 91 07 v 1 2 4 Se p 19 97 1 Yang - Mills classical solutions and fermionic zero modes from lattice calculations ∗

We study a series of problems in classical Yang-Mills theories using lattice methods. We first investigate SU(N) self-dual configurations on the torus with twisted boundary conditions. We also study the zero modes of the Dirac equation in topological non-trivial background Yang-Mills fields.

ar X iv : 0 70 7 . 40 46 v 1 [ m at h . A G ] 2 7 Ju l 2 00 7 CLIFFORD ’ S THEOREM FOR COHERENT SYSTEMS

Let C be an algebraic curve of genus g ≥ 2. We prove an analogue of Clifford’s theorem for coherent systems on C and some refinements using results of Re and Mercat.