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R. M. Iakhibbaev

Publications and source records attributed to R. M. Iakhibbaev.

15 recordsLinked to original sources
arXiv2026

Leading UV divergences of quantum corrections to Kähler superpotential in general $\mathcal{N}=1$ chiral model

Using the Bogoliubov-Parasiuk theorem we derive differential equations for the sum of leading UV divergences of the Kähler potential in the general $\mathcal{N}=1$ supersymmetric chiral theory. The obtained equations recover the limit of the renormalizable Wess-Zumino theory and also allow one to consider non-renormalizable chiral interactions. Some implications of the obtained equations are shown.

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arXiv2026

Effective potential in $SO(N)$ symmetric scalar field theories in curved spacetime

We derive recurrence relations for leading logarithmic all-loop quantum corrections in the case of $SO(N)$ symmetric scalar theory with an arbitrary potential in curved spacetime. On this basis, a system of renormalisation group (RG) equations in the general is obtained approach for the effective potential in the large $N$ limit. As a simple illustration, we analyse the case of power-like potentials in the Jordan frame and discuss their application to inflationary cosmology.

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arXiv2026

New Solutions for RG Equations in QCD

We construct simple analytical solutions of renormalization group equations for the running coupling and for the Green functions in QCD in the asymptotic regime. These solutions have an explicit form and subsequently sum up the leading, subleading, and so on logarithms in all orders of PT. They easily reproduce the inverse logarithm expansion and allow for further summation and improvement of the asymptotic behaviour.

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arXiv2026

Effective Potential in Subleading Logarithmic Approximation in Arbitrary Non-renormalizable Scalar Field Theory

Following the previously developed approach to the calculation of quantum corrections to the effective potential in arbitrary scalar field theories in the leading logarithmic approximation, we extended it to the next-to-leading order. Based on Bogoliubov-Parasiuk-Hepp-Zimmerman renormalization procedure and the Bogoliubov-Parasiuk theorem, we construct recurrence relations and renormalization group equations that allow one to sum up the leading and subleading logarithms in all orders of perturbation theory. The formalism is applicable to an arbitrary scalar potential, renormalizable or not. To verify the results, we compare them with a renormalizable model treated within the standard renormalization group approach.

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arXiv2026

Chiral effective potential in $4D$, $\mathcal{N}=4$ SYM theory

We consider $4D$, $\mathcal{N}=4$, $SU(N)$ super Yang-Mills theory formulated in terms of $\mathcal{N}=1$ superfields where the leading low-energy contributions to effective action are given by chiral effective potential. This effective potential is calculated in one- and higher-loop approximations. It is shown that this potential is automatically finite and proportional to the classical chiral potential. All quantum corrections are found explicitly and factored into a coefficient at the classical potential.

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arXiv2025

Chiral effective potential in $4D$, $\mathcal{N}=1$ supersymmetric gauge theories

We calculate the chiral effective superpotential in $4D$ $\mathcal{N}=1$, $SU(N)$ super Yang-Mills theory coupled to chiral matter in one- and two-loop approximations. It is found that the one-loop contribution to the chiral effective potential is always finite and is expressed in terms of a specific triangle integral. The two-loop contributions generated by purely chiral vertices turned out to be finite as well. The chiral effective potential stipulated by supergraphs with gauge superfield subgraphs is finite for the supergraphs with no divergent subgraphs. In the case of the finite $\mathcal{N}=2$ SYM theory, the two-loop chiral contributions to the effective action are significanlty simplified. The leading large $N$ behavior of the chiral effective superpotential in finite $\mathcal{N}=2$ super-Yang-Mills models with $SU(N)$ gauge symmetry is studied and it is shown that the exact form in the coupling constant of the chiral effective superpotential can be found.

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arXiv2025

Dark energy due to quantum corrections to effective potential

In this paper we calculate quantum corrections to the effective potential in different models of inflationary cosmology. We show that quantum corrections lead to a modification of the initial potential uplifting its value at the minimum, which can be interpreted as a cosmological constant/dark energy. We concentrate on the models of $α$-attractors and show that one can naturally get small values of the cosmological constant. In the model of quintessence, the same mechanism modifies the value of dark energy at the present time.

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arXiv2025

All-loop effective potential for arbitrary scalar models in curved space-time

In this paper we calculate the leading divergences of the effective potential for an arbitrary scalar theory on a curved spacetime background. Based on the recurrence relation between the leading poles following from the locality condition, we obtain a system of generalised renormalisation-group equations that can be studied numerically or analytically in some special cases. We study the simplest effective potentials for power-like models and give a comparison of them in the framework of cosmological phenomenology.

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arXiv2025

Three-loop chiral effective potential in the Wess-Zumino model

We calculate the three-loop contribution to the chiral effective potential in the massless Wess-Zumino model. It is shown that while the non-renormalisation theorem forbids divergent contributions to the chiral potential, in the massless case the finite corrections survive. There are only three three-loop supergraphs that give rise to a superfield effective action in the pure chiral sector. Two of them are UV finite while the third requires one-loop counterterm corresponding to the chiral field renormalisation.

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arXiv2023

Generalising holographic fishchain

In this paper we present an attempt to generalise the integrable Gromov-Sever models, the so-called fishchain models, which are dual to biscalar fishnets. We show that in any dimension they can be derived at least for some integer deformation parameter of the fishnet lattice. We focus in particular on the study of fishchain models in AdS$_7$ that are dual to the six-dimensional fishnet models.

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arXiv2023

Leading all-loop quantum contribution to the effective potential in the inflationary cosmology

In this paper, we have constructed quantum effective potentials and used them to study slow-roll inflationary cosmology. We derived the generalised RG equation for the effective potential in the leading logarithmic approximation and applied it to evaluate the potentials of the $T^2$ and $T^4$-models, which are often used in modern models of slow-roll inflation. We found that while the one-loop correction strongly affects the potential, breaking its original symmetry, the contribution of higher loops smoothes the behaviour of the potential. However, unlike the $ϕ^4$-case, we found that the effective potentials preserve spontaneous symmetry breaking when summing all the leading corrections. We calculated the spectral indices $n_s$ and $r$ for the effective potentials of both models and found that they are consistent with the observational data for a wide range of parameters of the models.

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arXiv2023

Leading all-loop quantum contribution to the effective potential in general scalar field theory

The RG equation for the effective potential in the leading log (LL) approximation is constructed which is valid for an arbitrary scalar field theory in 4 dimensions. The solution to this equation sums up the leading $\logϕ$ contributions to all orders of perturbation theory. In general, this is the second order nonlinear partial differential equation, but in some cases it can be reduced to the ordinary one. For particular examples, this equation is solved numerically and the LL effective potential is constructed. The solution has a characteristic discontinuity replacing the Landau pole typical for the $ϕ^4$ theory. For a power-like potential no new minima appear due to the Coleman-Weinberg mechanism.

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arXiv2021

Amplitudes in fishnet theories in diverse dimensions and Box ladder diagrams

We investigate properties of four point colour ordered scattering amplitudes in D=6 fishnet CFT. We show that such amplitudes are related via very simple relation to their D=4 counterparts considered previously in the literature. Exploiting this relation we obtain closed expression for such amplitudes and investigate its behaviour at weak and strong coupling. As by product of this investigation we also obtain generating function for on-shell D=6 Box ladder diagrams with l rungs.

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arXiv2020

Dual Conformal Symmetry and Iterative Integrals in Six Dimensions

In this article, we continue the investigation of hep-th 1611.02179 regarding iterative properties of dual conformal integrals in higher dimensions. In d=4, iterative properties of four and five point dual conformal integrals manifest themselves in the famous BDS ansatz conjecture. In hep-th 1611.02179 it was also conjectured that a similar structure of integrals may reappear in d=6. We show that one can systematically, order by order in the number of loops, construct combinations of d=6 integrals with 1/(p^2)^2 propagators with an iterative structure similar to the d=4 case. Such combinations as a whole also respect dual conformal invariance but individual integrals may not.

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