One-loop effective action in the $$ \mathcal{N} $$=2 supersymmetric massive Yang-Mills field theory

We consider the =2 supersymmetric massive Yang-Mills field theory formulated in the =2 harmonic superspace. We present various gauge-invariant forms of writing the mass term in the action (in particular, using the Stueckelberg superfield), which result in dual formulations of the theory. We develop a gaugeinvariant and explicitly supersymmetric scheme of the loop expansion of the superfield effective action beyond the mass shell. In the framework of this scheme, we calculate gauge-invariant and explicitly =2 supersymmetric one-loop counterterms including new counterterms depending on the Stueckelberg superfield. We analyze the component structure of one of these counterterms. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 1, pp. 22–40, October, 2008.     

Verifying a new identity for Green’s functions of the n=1 supersymmetric non-Abelian Yang-Mills theory with matter fields

We use the higher covariant derivative regularization to investigate a new identity for Green’s functions. It relates certain coefficients of the matter superfield vertex function for which one of the external matter legs is not chiral. Calculations in the first nontrivial order (for the two-loop vertex function) demonstrate that the new identity also holds in the non-Abelian Yang-Mills theory with matter fields. We demonstrate that the new identity follows because the three-loop integrals determining the Gell-Mann-Low function are integrals of total derivatives. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 2, pp. 270–281, August, 2008.     

Two-loop Gell-Mann-Low function of the <Emphasis Type="Italic">N</Emphasis>=1 supersymmetric Yang-Mills theory regularized by higher covariant derivatives

We calculate the two-loop Gell-Mann-Low function for the N=1 supersymmetric Yang-Mills theory regularized by higher covariant derivatives. We show that the integrals determining this function reduce to total derivatives and can be easily calculated analytically. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 3, pp. 398–414, June, 2008.     

Contribution of matter fields to the Gell-Mann-Low function for the $$\mathcal{N} = 1$$ supersymmetric Yang-Mills theory regularized by higher covariant derivatives

We use the Schwinger-Dyson equations and Slavnov-Tailor identities to obtain the contribution of matter fields to the Gell-Mann-Low function for the supersymmetric Yang-Mills theory regularized by higher covariant derivatives. We discuss the possible deviation of the result from the corresponding contribution to the exact Novikov-Shifman-Vainshtein-Zakharov β-function. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 3, pp. 441–460, March, 2007.     

Free-field resolutions of unitary representations of theN=2 virasoro algebra: I1

We construct a free-field resolution of unitary representations of theN=2 superconformal algebra. The resolution is degenerated by the action of one fermionic screening operator (which generates the “gravitational descendants” in the field theory picture). The irreducible representation is singled out from the free-field space as the cohomology of this screening operator. this paper is written at the request of the Editorial Board. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 121, No. 1, pp. 89–109, October, 1999.     

One-loop effective action for an arbitrary theory

Using the diagram technique, we obtain formulas for the divergent part of the one-loop effective action for an arbitrary minimal operator in four-dimensional curved space and for an arbitrary nonminimal operator in flat space.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 109, No. 2, pp. 215–231, November, 1996.     

Stationary points of the Yang-Mills action

We examine the structure of a recently discovered set of non-self-dual solutions of the Yang-Mills equations. These solutions have a symmetry that reduces the YM equations to a set of ODE's. The distinct solutions are indexed by two postive odd integers. We develop a scheme to approximate on a computer the solutions for small values of the indexing integers and present some numerical results. We then analyze the asymptotic behavior of the solutions as the indexing integers become large.     

Local gauge-invariant infrared regularization of Yang-Mills theory

We construct a local gauge invariant-infrared regularization for Yang-Mills theory based on a higher-derivative formulation of the model. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 2, pp. 213–219, February, 2008.     

Holographic relation between p-adic effective action and string field theory

We consider two holographically related theories. As the first (d + 1)-dimensional theory, we consider a model in which the (d + 1)-dimensional space is the direct product of ? ^d and the half-axis ?₊ and in which the kinetic operator has a nonlocal term induced by the nonlocal kinetic operator of the p-adic effective action. It turns out that the kinetic operator in the second, holographically related, d-dimensional theory is the kinetic operator of the string field theory effective action.     

Summation of diagrams in N=1 supersymmetric electrodynamics regularized by higher derivatives

For the massless N=1 supersymmetric electrodynamics regularized by higher derivatives, we partially sum the Feynman diagrams that define the divergent part of the two-point Green’s function and cannot be found from Schwinger—Dyson equations and Ward identities. The result can be written as a special identity for Green’s functions. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 3, pp. 385–401, March, 2006.     

The holomorphic effective action inN=2D=4 supergauge theories with various gauge groups

We consider the theory of hypermultiplets in arbitrary representations of arbitrary semisimple gauge groups coupled to gauge superfields. Using the N=2 harmonic superspace formulation of these models, we find the general structure of the holomorphic effective action depending on the gauge superfield with values in the Cartan subalgebra of the gauge algebra. We find explicit expressions for the effective actions in the cases where the hypermultiplets are in the fundamental and adjoint representations of SU(n), SO(n), and Sp(2n). Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 122, No. 3, pp. 444–455, April, 2000.     

Renormalization of the N=1 supersymmetric 4-dimensional nonlinear sigma model with higher derivatives

Institute of High-Current Electronics, Siberian Branch, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 77, No. 2, pp. 224–233, November, 1988.