arXiv subjects

Sergei Aleshin

Publications and source records attributed to Sergei Aleshin.

3 recordsLinked to original sources

arXiv2026

Construction of mirror pairs Calabi-Yau orbifolds of the Berglund-Hubsch type

In this paper we have developed general algorithm for finding all orbifolds of Berglund-Hubsch-type Calabi-Yau manifolds and their mirrors. An explicit construction is formulated for finding all admissible deformations and groups defining mirror pairs of orbifolds. Then using our algorithm for one of the Calabi-Yau manifolds, defined by a Fermat-type polynomial, we found all mirror pairs of orbifolds. For this model, for each pair of orbifolds, the number of generations and the number of singlets i.e. particles participating only in gravitational interactions (dark matter particles) were found.

hep-th↗

arXiv2023

Quantum properties of gauge theories with extended supersymmetry formulated in ${\cal N}=1$ superspace

We analyse quantum properties of ${\cal N}=2$ and ${\cal N}=4$ supersymmetric gauge theories formulated in terms of ${\cal N}=1$ superfields and investigate the conditions imposed on a renormalization prescription under which the non-renormalization theorems are valid. For this purpose in these models we calculate the two-loop contributions to the anomalous dimensions of all chiral matter superfields and the three-loop contributions to the $β$-functions for an arbitrary ${\cal N}=1$ supersymmetric subtraction scheme supplementing the higher covariant derivative regularization. We demonstrate that, in general, the results do not vanish due to the scheme dependence, which becomes essential in the considered approximations. However, the two-loop anomalous dimensions vanish if a subtraction scheme is compatible with the structure of quantum corrections and does not break the relation between the Yukawa and gauge couplings which follows from ${\cal N}=2$ supersymmetry. Nevertheless, even under these conditions the three-loop contribution to the $β$-function does not in general vanishes for ${\cal N}=2$ supersymmetric theories. To obtain the purely one-loop $β$-function, one should also chose an NSVZ renormalization prescription. The similar statements for the higher loop contributions are proved in all orders.

hep-th↗

arXiv2022

The $β$-function of supersymmetric theories from vacuum supergraphs: a three-loop example

We verify a method which allows to obtain the $β$-function of supersymmetric theories regularized by higher covariant derivatives by calculating only specially modified vacuum supergraphs. With the help of this method for a general renormalizable ${\cal N}=1$ supersymmetric gauge theory a part of the three-loop $β$-function depending on the Yukawa couplings is constructed in the general $ξ$-gauge. The result is written in the form of an integral of double total derivatives with respect to the loop momenta. It is demonstrated that all gauge dependent terms cancel each other in agreement with the general statements. Taking into account that the result in the Feynman gauge (found earlier) coincides with the one obtained by the standard technique, this fact confirms the correctness of the considered method by a highly nontrivial multiloop calculation.

hep-th↗