arXiv subjects

A. V. Ivanov

Publications and source records attributed to A. V. Ivanov.

At least 19 recordsLinked to original sources

arXiv2026

Renormalization, cutoff, and gluing for a quartic model with boundary

In this paper, we study the renormalization of a three-dimensional quartic model on a compact connected Riemannian manifold with a boundary. We show that, in addition to the standard shift of the mass parameter, it is necessary to take into account boundary contributions involving singular coefficients. This indicates the need to extend the classical action within the framework of standard renormalization theory. The requirements of consistency regarding the gluing of manifolds lead to renormalization of an operator on the boundary.

hep-th↗

arXiv2026

Renormalization aspects of the Yang-Mills theory with a cutoff

The paper discusses renormalization aspects of the quantum four-dimensional Yang-Mills theory with a cutoff regularization in the coordinate representation. The background field method is used to formulate a generating functional, and the regularization is introduced through quasi-local probabilistic averaging. Two main types of regularization are proposed: strong deformation, which consists in averaging fluctuation fields, and weak deformation, which is a covariant generalization of the first case with respect to gauge transformations of the background field. We study singular contributions for the first two quantum corrections in this paper and compare them in detail with the case of dimensional regularization. The consistency of the action and the equation of motion after introducing the regularization and making a renormalization procedure is analyzed. New counter-vertices are studied, in particular their locality properties and dependence on the regularization parameter.

hep-th↗

arXiv2026

Quasi-local probability averaging in the context of cutoff regularization

In this paper, we study the properties of averaged fundamental solutions of a special type for Laplace operators in the Euclidean space of an arbitrary dimension. We consider a class of kernels suitable for probabilistic averaging, and propose new representations for the deformed fundamental solutions and their values at zero. In addition, we give examples related to specific quantum field models in the context of studying renormalization properties.

math-ph↗

arXiv2026

Three-loop functions for a quartic model with a cutoff

This paper presents numerical values for auxiliary integrals and coefficients of the beta function in the three-loop approximation for a four-dimensional model with a quartic interaction, using a special type of regularization function. The values are compared to previously obtained results.

hep-th↗

arXiv2025

Summation of power singularities

In this paper, we investigate an example of summation of non-logarithmic singularities of a specific type in a two-dimensional non-linear sigma model. As a result of the study, we obtained an explicit formula, which, upon formal expansion in terms of the coupling constant, reproduces a particular part of the quantum action. Additionally, the paper introduces a new auxiliary function and discusses some of its properties.

hep-th↗

arXiv2025

Three-loop singularity structure for a non-linear sigma model

The paper is devoted to the three-loop renormalization of the effective action for a two-dimensional non-linear sigma model using the background field method and a cutoff regularization in the coordinate representation. The coefficients of the renormalization constant and the necessary auxiliary vertices are found, as well as the asymptotic expansions of all three-loop diagrams, and their dependence on the type of regularizing function. A comparison is also made with the standard case of cutoff in the momentum representation.

hep-th↗

arXiv2025

Searching for Light Dark Matter and Dark Sectors with the NA64 experiment at the CERN SPS

Since its approval in 2016, NA64 has pioneered light dark matter (LDM) searches with electron, positron, muon, and hadron beams. The experiment has successfully met its primary objectives, as outlined in the EPPS input (2018), and even exceeded them, producing results that demonstrate its ability to operate in a near-background-free environment. The Physics Beyond Collider (PBC) initiative at CERN recognizes NA64's contributions as complementary and worthy of continued exploration. Its key advantage over beam-dump approaches is that the signal rate scales as the square of the coupling rather than the fourth power, reducing the required number of beam particles for the same sensitivity. To fully exploit the NA64 physics potential, an upgrade during LS3 will enable the experiment to run in background-free mode at higher SPS beam rates. Planned upgrades include: (a) improved detector hermeticity with a new veto hadron calorimeter, (b) enhanced particle identification with a synchrotron radiation detector, and (c) increased beam rates via upgraded electronics. With the recently strengthened NA64 collaboration, stable operations and timely data analysis are planned for LHC Run 4. The expected beam exposures are approximately 1e13 electrons, 1e11 positrons (at 40 and 60 GeV), and 2e13 muons on target. This will allow NA64 to explore new LDM parameter space, with the potential for discovery or conclusive exclusion of many well-motivated models.

hep-ex↗

arXiv2025

An etude on a renormalization

In this paper, we study renormalization, that is, the procedure for eliminating singularities, for a special model using both combinatorial techniques in the framework of working with formal series, and using a limit transition in a standard multidimensional integral, taking into account the removal of the singular components. Special attention is paid to the comparative analysis of the two views on the problem. It is remarkably that the divergences, which have the same form in one approach, acquire a different nature in another approach and lead to interesting consequences. A special deformation of the spectrum is used as regularization.

math-ph↗

arXiv2024

Effective actions, cutoff regularization, quasi-locality, and gluing of partition functions

The paper studies a regularization of the quantum (effective) action for a scalar field theory in a general position on a compact smooth Riemannian manifold. As the main method, we propose the use of a special averaging operator, which leads to a quasi-locality and is a natural generalization of a cutoff regularization in the coordinate representation in the case of a curved metric. It is proved that the regularization method is consistent with a process of gluing of manifolds and partition functions, that is, with the transition from submanifolds to the main manifold using an additional functional integration. It is shown that the method extends to other models, and is also consistent with the process of multiplicative renormalization. Additionally, we discuss issues related to the correct introduction of regularization and the locality.

math-ph↗

arXiv2024

Three-loop renormalization of the quantum action for a five-dimensional scalar cubic model with the usage of the background field method and a cutoff regularization

The paper studies the quantum action for the five-dimensional real $ϕ^3$-theory in the case of a general formulation using the background field method. The three-loop renormalization is performed with the usage of a cutoff regularization in the coordinate representation. The explicit form of the first three coefficients for the renormalization constants is presented. The absence of non-local singular contributions and partial results for the fourth correction are discussed.

hep-th↗

arXiv2024

On a criterion for a cutoff regularization in the coordinate representation

The paper discusses an applicability criterion for a cutoff regularization in the coordinate representation in the Euclidean space with a dimension larger than two. It is shown that the set of functions satisfying the criterion is not empty. As an example, an explicit function is presented. It is proved by explicit construction that there are functions satisfying the criterion in a stronger formulation.

math-ph↗

arXiv2024

Three-loop renormalization of the quantum action for a four-dimensional scalar model with quartic interaction with the usage of the background field method and a cutoff regularization

The paper studies the quantum action for the four-dimensional real $ϕ^4$-theory in the case of a general formulation using the background field method. The three-loop renormalization is performed with the usage of a cutoff regularization in the coordinate representation. The absence of non-local singular contributions and the correctness of the renormalization $\mathcal{R}$-operation on the example of separate three-loop diagrams are also discussed. The explicit form of the first three coefficients for the renormalization constants and for the $β$-function is presented. Consistency with previously known results is shown.

hep-th↗

arXiv2023

Mellin$-$Barnes Transformation for Two-Loop Master-Diagram

In the paper, we obtain an expression for a two-loop master-diagram by using the Mellin$-$Barnes transformation. In the two-dimensional case we managed to factorize the answer and write it as a bilinear combination of hypergeometric functions ${}_3F_2$.

hep-th↗

arXiv2023

On Two-Loop Effective Action of 2D Sigma Model

In this paper, we study two-loop contribution to the effective action of a two-dimensional sigma model. We derive a new formula, which can be applicable to a regularization of general type. As examples, we obtain known results for dimensional regularization and investigate new types of cutoff one. Also, we discuss non-local contributions and restrictions on the regularization.

hep-th↗

arXiv2023

On Local Heat Kernel

The paper is devoted to a local heat kernel, which is a special part of the standard heat kernel. Locality means that all considerations are produced in an open convex set of a smooth Riemannian manifold. We study such properties and concepts as uniqueness, a symmetry of the Seeley-DeWitt coefficients, extension on the whole manifold, a family of special functions, and the late-time asymptotics with the use of the path integral formulation.

math-ph↗

arXiv2023

Ordered Exponential and Its Features in Yang-Mills Effective Action

In this paper we discuss some non-trivial relations for ordered exponentials on smooth Riemannian manifolds. As an example of application, we study a dependence of the four-dimensional quantum Yang-Mills effective action on the background filed and gauge transformations. Also, we formulate some open questions about a structure of divergences.

hep-th↗

arXiv2022

Anomaly inflow for local boundary conditions

We study the $η$-invariant of a Dirac operator on a manifold with boundary subject to local boundary conditions with the help of heat kernel methods. In even dimensions, we relate this invariant to $η$-invariants of a boundary Dirac operator, while in odd dimension, it is expressed through the index of boundary operators. We stress the necessity of the strong ellipticity condition for the applicability of our methods. We show that the Witten--Yonekura boundary conditions are not strongly elliptic, though they are very close to strongly elliptic ones.

hep-th↗

arXiv2022

Explicit Cutoff Regularization in Coordinate Representation

In this paper, we study a special type of cutoff regularization in the coordinate representation. We show how this approach unites such concepts and properties as an explicit cut, a spectral representation, a homogenization, and a covariance. Besides that, we present new formulae to work with the regularization and give additional calculations of the infrared asymptotics for some regularized Green's functions, appearing in the pure four-dimensional Yang-Mills theory and in the standard two-dimensional Sigma-model.

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