Abstract
The effective diagram technique based on the Schwinger-Dyson equations is constructed for N=1 SQED with N_f flavors, regularized by higher derivatives. Using these effective diagrams, it is possible to derive the exact NSVZ relation between the beta-function and the anomalous dimension of the matter superfields exactly in all loops, if the renormalization group functions are defined in terms of the bare coupling constant. In particular, we verify that all integrals which give the beta-function defined in terms of the bare coupling constant are integrals of double total derivatives and prove some identities relating Green functions.
Highlights
The existence of ultraviolet divergences is a long standing problem of quantum field theory
It is possible to derive the exact NSVZ relation between the βfunction and the anomalous dimension of the matter superfields exactly in all loops, if the renormalization group functions are defined in terms of the bare coupling constant
Assuming that the other contributions vanish we obtain the NSVZ relation for the renormalization group functions defined in terms of the bare coupling constant
Summary
The existence of ultraviolet divergences is a long standing problem of quantum field theory. Quantum corrections obtained with the higher covariant derivative regularization in supersymmetric theories appear to have an interesting feature: the β-function defined in terms of the bare coupling constant is given by integrals of total derivatives with respect to a loop momentum [59,60,61,62] and even by integrals of double total derivatives [63,64,65,66]. In the non-Abelian case the calculations with the higher covariant derivative regularization were performed only in the one- and two-loop approximations, where the β-function is scheme-independent In both cases the β-function appears to be given by integrals of double total derivatives and coincide with the NSVZ expression.
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