This paper discusses some interesting features of quantum corrections in N = 1 supersymmetric theories, which have been discovered analyzing calculations made with the higher covariant derivative regularization. In particular, the author argues that all integrals, defining the Gell-Mann-Low function in supersymmetric theories, are integrals of total derivatives. As a consequence, possibly there are some interesting identities, which restrict Green functions and do not follow from usual Slavnov-Taylor identities.

Existence of ultraviolet divergences is one of the most important problems of the quantum field theory. Although the superstring theories seem to be free from divergences (Green et al., 1987), most theories, which describe the quark-lepton physics, are divergent. An important step to solve this problem is the discovery of the supersymmetry. It is well-known that the ultraviolet behavior of supersymmetric theories is better due to some non-renormalization theorems (West, 1983). In particular, there are no quadratic divergencies and no divergent contributions to the superpotential in globally supersymmetric theories.

All these attractive features are very useful for construction of realistic models (Mohapatra, 2003). For example, the absence of quadratic divergences solves the problem of the Higgs mass renormalization. Existence of supersymmetry in the standard model is confirmed indirectly by precise measurement of three coupling constants and investigating their evolution by the renorm group equations. The result is that in the supersymmetric version of the standard model, the coupling constants coincide at some energy scale, i.e., in agreement with the grand unification. However, in order to include super gravity, the supersymmetry should be local. Such super gravity theories have a lot of attractive features from the phenomenological point of view (Nilles, 1984; and Lahanas and Nanopoulos, 1987). Unfortunately, theories with local supersymmetry seem to be non-renormalizable. Investigation of their quantum properties is certainly very interesting.

As a rule in non-supersymmetric theories, all possible divergent terms, which are not forbidden by symmetries, appear in the effective action. However, in supersymmetric theories, we can encounter some surprises. In particular, the ultraviolet behavior of supersymmetric theories can be better than that seems at first sight. For example, in Novikov et al. (1986), proposed the form of the exact b-function in N = 1 supersymmetric theories have been proposed. This b-function, called the exact Novikov-Shifman-Vainshtein-Zakharov (NSVZ) b-function, is

Physics Journal, Quantum Corrections, Supersymmetry, Gell-Mann-Low function, Slavnov-Taylor identities, Schwinger-Dyson Equations, Higgs Mass Renormalization, Novikov-Shifman-Vainshtein-Zakharov, NSVZ, Chiral Scalar Matter Superfields, Nielsen-Kallosh Ghosts.