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ONE-LOOP DIVERGENCES FOR THE FIELD OF SPIN 3 ON A DE SITTER BACKGROUND IN NONMINIMAL GAUGE // Tomsk State Pedagogical University Bulletin. 2012. Issue 13 (128). P. 130-133

We consider the eld of spin 3 on the de Sitter background in two dimensions and calculate the the divergent part of the one-loop effective action in a nonminimal gauge. For this purpose we construct a simple formula for the b2 coecient of an arbitrary second order differential operator with small nonminimal terms. Using this formula we nd that the divergent part of one-loop effective action for the considered theory is gauge independent.

Keywords: higher spins, Minakshisundaram-De Witt-Seeley coecients, (anti)-de Sitter space

Derivation of the exact NSVZ beta-function using effective diagrams // Tomsk State Pedagogical University Bulletin. 2012. Issue 13 (128). P. 149-154

Using Scwinger-Dyson equation we prove that the beta-function for N = 1 supersymmetric electrodynamics is given by integrals of double total derivatives. This allows to calculate one of the loop integrals and obtain the exact NSVZ beta-function, which relates the beta-function and the anomalous dimension of the matter superfield.

Keywords: supersymmetry, supergraphs, NSVZ beta-function

NSVZ SCHEME AND THE REGULARIZATION BY HIGHER DERIVATIVES // Tomsk State Pedagogical University Bulletin. 2014. Issue 12 (153). P. 238-242

The NSVZ scheme is constructed in all orders for the renormalization group functions defined in terms of the renormalized coupling constant for Abelian N = 1 supersymmetric theories regularized by higher derivatives. For the other renormalization prescriptions the scheme-independent consequences of the NSVZ relation are investigated. It is explained, why for the renormalization group functions defined in terms of the bare coupling constant the NSVZ relation is valid for all renormalization prescriptions in the case of using the higher derivative regularization.

Keywords: supersymmetry, renormalization, β-function, anomalous dimension