Towards proof of new identity for Green functions in N=1 supersymmetric electrodynamics

For the N=1 supersymmetric massless electrodynamics, regularized by higher derivatives, we describe a method, by which one can try to prove the new identity for the Green functions, which was proposed earlier. Using this method we show that some contribution to the new identity are really 0.Comment: 16 pages, 1 figure, an error corrected, significant change

Background field formalism and construction of effective action for N=2, d=3 supersymmetric gauge theories

We review the background field method for three-dimensional Yang-Mills and Chern-Simons models in N=2 superspace. Superfield proper time (heat kernel) techniques are developed and exact expressions of heat kernels for constant backgrounds are presented. The background field method and heat kernel techniques are applied for evaluating the low-energy effective actions in N=2 supersymmetric Yang-Mills and Chern-Simons models as well as in N=4 and N=8 SYM theories.Comment: 1+30 pages, dedicated to the 60 year Jubilee of Professor D.I. Kazakov; references added. arXiv admin note: substantial text overlap with arXiv:1010.496

Finite Unified Theories and the Higgs boson

All-loop Finite Unified Theories (FUTs) are very interesting N = 1 supersymmetric Grand Unified Theories (GUTs) realising an old field theory dream, and moreover have a remarkable predictive power due to the required reduction of couplings. Based on this theoretical framework phenomenologically consistent FUTs have been constructed. Here we review two FUT models based on the SU(5) gauge group, which can be seen as special, restricted and thus very predictive versions of the MSSM. We show that from the requirement of correct prediction of quark masses and other experimental constraints a light Higgs-boson mass in the range M_h ~ 121 - 126 GeV is predicted, in striking agreement with recent experimental results from ATLAS and CMS. The model furthermore naturally predicts a relatively heavy spectrum with colored supersymmetric particles above ~ 1.5 TeV in agreement with the non-observation of those particles at the LHC.Comment: 13 pages, 5 figures. Proceedings devoted to the Scientific and Human Legacy of Julius Wess, initiated by the JW2011 Workshop, August 27 - 28, 2011, Donji Milanovac, Serbi