arXiv subjects
Publications and source records attributed to K. Stepanyantz.
The Adler function D is found {\em exactly} in supersymmetric QCD. Our exact formula relates D(Q^2) to the anomalous dimension of the matter superfields γ(α_s(Q^2)). En rout we prove another theorem: the absence of the so-called singlet contribution to D. While such singlet contributions are present in individual supergraphs, they cancel in the sum.
For the massless N=1supersymmetric electrodynamics, regularized by higher derivatives, the Feynman diagrams, which define the divergent part of the two-point Green function and can not be found from Schwinger-Dyson equations and Ward identities, are partially summed. The result can be written as a special identity for Green functions.
Two-loop $β$-function and anomalous dimension are calculated for N=1 supersymmetric quantum electrodynamics, regularized by higher derivatives in the minimal subtraction scheme. The result for two-loop contribution to the $β$-function appears to be equal to 0, does not depend on the form of regularizing term and does not lead to anomaly puzzle. Two-loop anomalous dimension can be also made independent on parameters of higher derivative regularization by a special choice of subtraction scheme.
Divergent part of the one-loop effective action for the Yang-Mills theory in a special gauge containing forth degrees of ghost fields and allowing addition of BRST-invariant mass term is calculated by the generalized t'Hooft-Veltman technique. The result is BRST-invariant and defines running mass, coupling constant and parameter of the gauge.
An expression for the exact (nonperturbative) effective action of $N$=1 supersymmetric gauge theories is proposed, supposing, that all particles except for the gauge bosons are massive. Analysis of its form shows, that instanton effects in the supersymmetric theories can lead to the quark confinement. The typical scale of confinement in MSSM QCD, calculated from the first principles, is in agreement with the experimental data. The proposed explanation is quite different from the dual Higgs mechanism.
We discuss the ways of constructing the exact superpotential for N=1 supersymmetric theories and propose a new approach. As a consequence, a new structure of the superpotential is found.
We investigate nonperturbative effects in N=1 supersymmetric theories and propose a new expression for the effective action, which correctly reproduces quantum anomalies and agrees with the transformation law of instanton measure. Actually the result is a nonperturbative extension of Veneziano-Yankielowitch effective Lagrangian. The possibility of integrating out the gluino condensate is discussed.
We investigate nonperturbative effects in N=1 and N=2 supersymmetric theories using a relation between perturbative and exact anomalies as a starting point. For N=2 supersymmetric SU(n) Yang-Mills theory we derive the general structure of the Picard-Fuchs equations; for N=1 supersymmetric Yang-Mills theories we find holomorphic part of the superpotential (with gluino condensate) exactly.
Using an analogy between Bogomol'nyi bound and the harmonic oscillator in quantum mechanics we propose a possible explanation of the coupling constant numerical value at the grand unification scale. It is found to be $1/8π$.
Using as an example the Einstein gravity with the cosmological constant, we discuss the calculation of renormalization group functions off shell. We found, that gauge dependent terms should be absorbed by the nonlinear renormalization of metric. Nevertheless, some terms can be included in the renormalization of Newton's constant. This ambiguity in the renormalization prescription is discussed.
We explicitly calculate one-loop divergences for an arbitrary field theory model using the higher derivative regularization and nonsingular gauge condition. They are shown to agree with the results found in the dimensional regularization and do not depend on the form of regularizing term. So, the consistency of the higher derivative regularization is proven at the one-loop level. The result for the Yang-Mills theory is reproduced.
We present master formulas for the divergent part of the one-loop effective action for an arbitrary (both minimal and nonminimal) operators of any order in the 4-dimensional curved space. They can be considered as computer algorithms, because the one-loop calculations are then reduced to the simplest algebraic operations. Some test applications are considered by REDUCE analytical calculation system.
We present master formulas for the divergent part of the one-loop effective action for a minimal operator of any order in the 4-dimensional curved space and for an arbitrary nonminimal operator in the flat space.