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Alexander N. Manashov

Publications and source records attributed to Alexander N. Manashov.

13 recordsLinked to original sources
arXiv2026

Correction exponents in the chiral Heisenberg model at $1/N^2$: singular contributions and operator mixing

We calculate the correction exponents in the chiral Heisenberg model in the $1/N$ expansion. These exponents are related to the slopes of $β$ functions at the phase transition point. We present the results at order $1/N^2$ and check that they agree with the results of the $ε$ expansion near $d = 4$. We find that one of the correction exponents diverges as $d \to 3$. We argue that the appearance of the pole is a rather general phenomenon and is associated with operator mixing involving the system of four-fermion operators. After analyzing the operator mixing structure, we propose a resummation procedure which modifies the exponents already at leading order. We also perform calculations directly in the three-dimensional model and find complete agreement with the resummed exponents.

hep-th↗
arXiv2026

Resummation of small-spin singularities in anomalous dimensions of twist-two operators

Anomalous dimensions of leading-twist operators in QCD play an important role in precision predictions for high-energy processes, since they govern the scale evolution of parton distributions. Their analytic structure as a function of spin is particularly important due to the complexity of higher-loop computations. In these proceedings, we discuss the resummation of the certain type of such singularities that share common features with those appearing in the quark flavor-nonsinglet sector of QCD. Our main focus is on the interplay between Gross-Neveu-Yukawa model in $ε$ expansion and Gross-Neveu in $1/N$ expansion. Such resummation allows one to predict the higher-loop singular behavior and reveals connections with the conformal Regge theory and recent studies of detector operators in QCD and various conformal field theories.

hep-th↗
arXiv2024

The two-loop coefficient functions for double deeply virtual Compton scattering

Making use of conformal symmetry of large-$n_f$ QCD in $d=4-2ε$ dimensions at the Wilson-Fischer fixed point, we calculate the two-loop coefficient functions in the operator product expansion of two electromagnetic currents in general kinematics with two different photon virtualities. This result is necessary for the description of the double deeply virtual Compton scattering to the next-to-next-to-leading order accuracy, but is also interesting for a range of other two-photon processes. We present analytic expression for the coefficient function in momentum fraction space in the $\overline{\text{MS}}$ scheme and study its numerical impact on the Compton form factors for a simple model of the generalized parton distributions. The calculated corrections turn out to be large and are significant for the kinematics of proposed experiments.

hep-ph↗
arXiv2021

Completeness of SoV Representation for $\mathrm{SL}(2,\mathbb R)$ Spin Chains

This work develops a new method, based on the use of Gustafson's integrals and on the evaluation of singular integrals, allowing one to establish the unitarity of the separation of variables transform for infinite-dimensional representations of rank one quantum integrable models. We examine in detail the case of the $\mathrm{SL}(2,\mathbb R)$ spin chains.

math-ph↗
arXiv2020

On Complex Gamma-Function Integrals

It was observed recently that relations between matrix elements of certain operators in the ${\rm SL}(2,\mathbb R)$ spin chain models take the form of multidimensional integrals derived by R.A. Gustafson. The spin magnets with ${\rm SL}(2,\mathbb C)$ symmetry group and ${\rm L}_2(\mathbb C)$ as a local Hilbert space give rise to a new type of $Γ$-function integrals. In this work we present a direct calculation of two such integrals. We also analyse properties of these integrals and show that they comprise the star-triangle relations recently discussed in the literature. It is also shown that in the quasi-classical limit these integral identities are reduced to the duality relations for Dotsenko-Fateev integrals.

math-ph↗
arXiv2018

On operator mixing in fermionic CFTs in non-integer dimensions

We consider renormalization of four-fermion operators in the critical QED and $SU(N_c)$ version of Gross--Neveu--Yukawa model in non-integer dimensions. Since the number of mixing operators is infinite, the diagonalization of an anomalous dimension matrix becomes a nontrivial problem. At leading order, construction of eigen-operators is equivalent to solving certain three-term recurrence relations. We find analytic solutions of these recurrence relations that allows to determine the spectrum of anomalous dimensions and study their properties.

hep-th↗
arXiv2018

On the separation of variables for the modular XXZ magnet and the lattice Sinh-Gordon models

We construct the generalised Eigenfunctions of the entries of the monodromy matrix of the $N$-site modular XXZ magnet and show, in each case, that these form a complete orthogonal system in $L^2(\mathbb{R}^N)$. In particular, we develop a new and simple technique, allowing one to prove the completeness of such systems. As a corollary of out analysis, we prove the Bystko-Teschner conjecture relative to the structure of the spectrum of the $\boldsymbol{ \texttt{B} }(\la)$-operator for the odd length lattice Sinh-Gordon model.

math-ph↗
arXiv2018

Integrability in heavy quark effective theory

It was found that renormalization group equations in the heavy-quark effective theory (HQET) for the operators involving one effective heavy quark and light degrees of freedom are completely integrable in some cases and are related to spin chain models with the Hamiltonian commuting with the nondiagonal entry $C(u)$ of the monodromy matrix. In this work we provide a more complete mathematical treatment of such spin chains in the QISM framework. We also discuss the relation of integrable models that appear in the HQET context with the large-spin limit of integrable models in QCD with light quarks. We find that the conserved charges and the "ground state" wave functions in HQET models can be obtained from the light-quark counterparts in a certain scaling limit.

hep-th↗
arXiv2018

${\rm SL}(2,\mathbb{C})$ Gustafson Integrals

It was shown recently that many of the Gustafson integrals appear in studies of the ${\rm SL}(2,\mathbb{R})$ spin chain models. One can hope to obtain a generalization of the Gustafson integrals considering spin chain models with a different symmetry group. In this paper we analyse the spin magnet with the ${\rm SL}(2,\mathbb{C})$ symmetry group in case of open and periodic boundary conditions and derive several new integrals.

math-ph↗
arXiv2017

Correction exponents in the Gross - Neveu - Yukawa model at $1/N^2$

We calculate the critical exponents $ω_\pm$ in the $d$-dimensional Gross-Neveu model in $1/N$ expansion with $1/N^2$ accuracy. These exponents are related to the slopes of the $β$-functions at the critical point in the Gross - Neveu - Yukawa model. They have been computed recently to four loops accuracy. We checked that our results are in complete agreement with the results of the perturbative calculations.

hep-th↗
arXiv2014

Deeply Virtual Compton Scattering to the twist-four accuracy: Impact of finite-$t$ and target mass corrections

We carry out the first complete calculation of kinematic power corrections $\sim t/Q^2$ and $\sim m^2/Q^2$ to several key observables in Deeply Virtual Compton Scattering. The issue of convention dependence of the leading twist approximation is discussed in detail. In addition we work out representations for the higher twist corrections in terms of double distributions, Mellin-Barnes integrals and also within a dissipative framework. This study removes an important source of uncertainties in the QCD predictions for intermediate photon virtualities $Q^2\sim 1$-$5\,{\rm GeV}^2$ that are accessible in the existing and planned experiments. In particular the finite-$t$ corrections are significant and must be taken into account in the data analysis.

hep-ph↗
arXiv2006

R-Matrix and Baxter Q-Operators for the Noncompact SL(N,C) Invariant Spin Chain

The problem of constructing the $SL(N,\mathbb{C})$ invariant solutions to the Yang-Baxter equation is considered. The solutions ($\mathcal{R}$-operators) for arbitrarily principal series representations of $SL(N,\mathbb{C})$ are obtained in an explicit form. We construct the commutative family of the operators $\mathcal{Q}_k(u)$ which can be identified with the Baxter operators for the noncompact $SL(N,\mathbb{C})$ spin magnet.

nlin.SI↗