Konstantin Viktorovich Stepanyantz

A bstract: We employ the harmonic superspace methods to study a six-dimensional 𝒩 = (1 , 0) supersymmetric gauge theory with higher derivatives coupled to a hypermultiplet in the adjoint representation. By introducing a certain non-minimal interaction between the gauge multiplet and the hypermultiplet, we demonstrate that the one-loop divergences in gauge superfield sector, which are present in the conventional formulation, are canceled. The resulting theory is off-shell one-loop finite in this sector, while preserving the gauge invariance and 𝒩 = (1 , 0) supersymmetry. The cancelation mechanism is explicitly verified using both the background field method and the supergraph techniques. Thus, we present an example of the higher-derivative supersymmetric gauge theory in six dimensions which is finite in the vector multiplet sector.

The group of finite renormalizations relating various renormalization prescriptions is considered as an infinite dimensional Lie group. The corresponding Lie algebra is constructed, and the Abelian subgroup corresponding to the changing of the renormalization point is studied. It is demonstrated that it can be used for obtaining all-order exact expressions for the renormalization constants relating them to the renormalization group functions.

We investigate the structure of renormalization constants within the MS-like renormalization prescriptions for a version of dimensional regularization in w

Using the harmonic superspace approach, we perform a comprehensive study of the structure of divergences in the higher-derivative 6 D , N = ( 1 , 0 ) supersymmetric Yang-Mills theory coupled to the hypermultiplet in the adjoint representation. The effective action is constructed in the framework of the superfield background field method with the help of the N = ( 1 , 0 ) supersymmetric higher-derivative regularization scheme which preserves all symmetries of the theory. The one-loop divergences are calculated in a manifestly gauge invariant and 6 D , N = ( 1 , 0 ) supersymmetric form, hopefully admitting a generalization to higher loops. The β function in the one-loop approximation is found and analyzed. In particular, it is shown that the one-loop β function for an arbitrary regulator function is specified by integrals of double total derivatives in momentum space, like it happens in 4 D , N = 1 superfield gauge theories. This points to the potential possibility to derive the Novikov-Shifman-Vainshtein-Zakharov-like exact β function in the considered theory. Published by the American Physical Society 2025

For the minimal supersymmetric Standard Model, from the gauge couplings, Yukawa couplings, and the coefficient μ in the part of the superpotential quadratic in the Higgs superfields, we construct combinations which (for certain renormalization prescriptions) do not depend on the renormalization point in all loops. In other words, these combinations are the renormalization group invariants. Similar invariants are also constructed for the next-to-minimal supersymmetric Standard Model. The derivation is based on the nonrenormalization of the superpotential and the Novikov-Shifman-Vainshtein-Zakharov equations. We argue that the scale invariance of the considered combinations takes place in the class of the higher derivatives + minimal subtractions of logarithms scheme. This fact has been verified in the lowest orders, up to and including the one in which the dependence on the renormalization prescription becomes essential. It is also demonstrated that in the DR ¯ scheme the renormalization group invariance does not take place starting from the approximation, where the scheme dependence manifests itself.

Some properties of quantum corrections in various supersymmetric theories revealed with the help of the higher covariant derivative regularization are brie