arXiv subjects

Pavel Meshcheriakov

Publications and source records attributed to Pavel Meshcheriakov.

6 recordsLinked to original sources

arXiv2026

Regge trajectories from the adjoint sector of Matrix Quantum Mechanics

We reexamine the large $N$ limit of SU$(N)$ symmetric quantum mechanics of a Hermitian matrix whose singlet sector is well known to be exactly solvable via free fermions. When the Fermi level approaches a maximum of the potential, there is critical behavior corresponding to string theory in two dimensions. We uncover new phenomena in the adjoint sector by solving the Marchesini-Onofri equation both numerically and analytically using semiclassical approximations: at criticality, the spectrum is governed by Regge trajectories with energy eigenvalues growing according to $Δ^2 \sim n/ α'$. In the dual 2D string theory, we interpret these states as oscillatory excitations of a ``short'' folded open string. Up to sub-leading corrections, this Regge behavior is essentially universal and is insensitive to the particular potential we choose to approach criticality. Slightly away from criticality, the highly excited states transition into ``long strings'' that extend far into the Liouville direction.

hep-th↗

arXiv2025

Analytical results for large-$N_c$ scalar QCD$_2$

We study large-$N_c$ scalar QCD$_2$, a $1+1$-dimensional confining gauge theory with fundamental scalar quarks, whose meson spectrum is governed by a Bethe-Salpeter equation structurally parallel to the 't Hooft equation. Exploiting this structural analogy, we develop a nonperturbative analytic framework, based on integrability and inspired by the Fateev-Lukyanov-Zamolodchikov (FLZ) method, originally devised for the 't Hooft model and later extended in our previous works. Notably, the same Bethe-Salpeter equation also arises in the description of interchain mesons in the doubled Ising model coupled via a spin-spin interaction term. Within the FLZ approach, we find spectral sums and derive a systematic large-$n$ WKB expansion for the meson spectrum. The analytic results reproduce the expected behavior in key asymptotic regimes, such as the near-critical limit $m\to g/\sqrtπ$ and the heavy-quark regime $m\gg g$, and are in good agreement with numerical data. Finally, by analytically continuing the mass parameter into the complex plane, we uncover two infinite families of singularities where individual mesons become massless, suggesting a hidden connection to nontrivial Conformal Field Theories.

hep-th↗

arXiv2025

Meson mass spectrum in Ising Field Theory

We study the two-particle approximation of the Ising Field Theory (IFT), formulated in terms of the Bethe-Salpeter (BS) equation. Derived by Fonseca and Zamolodchikov as a systematic realization of the McCoy-Wu approach, this equation captures confinement by modeling ``mesons'' as bound states of two Majorana fermions (``quarks''), in a way analogous to the integral equation in the 't Hooft model. Despite its approximate nature, the BS equation provides remarkably accurate predictions for the mass spectrum of stable mesons across a wide range of parameters. Motivated by the striking structural similarity between the BS equation in IFT and the 't Hooft equation in two-dimensional QCD, we develop a new non-perturbative analytical framework inspired by the method of Fateev, Lukyanov, and Zamolodchikov (FLZ). Within this approach, we compute spectral sums and systematically derive the large-$n$ WKB expansion for the Bethe-Salpeter equation, which governs the spectrum of an infinite tower of mesons. We further examine how our analytical results capture the known behavior of the spectrum in well-studied asymptotic regimes, such as the $E_8$ limit and the free-fermion point, where exact solutions are available for comparison. Finally, we discuss how the obtained spectral data admit a natural analytic continuation to complex values of the parameters -- an extension that was one of the primary motivations for this work.

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arXiv2025

Meson mass spectrum in QCD$_2$ 't Hooft's model

We study the spectrum of meson masses in large $N_c$ QCD$_2$ governed by celebrated 't Hooft's integral equation. We generalize analytical methods proposed by Fateev, Lukyanov and Zamolodchikov to the case of arbitrary, but equal quark masses $m_1=m_2.$ Our results include analytical expressions for spectral sums and systematic large-$n$ expansion. We also study the spectral sums in the chiral limit and the heavy quark limit and find a complete agreement with known results.

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arXiv2025

QCD$_2$ 't Hooft model: 2-flavour mesons spectrum

We continue analytical study of the meson mass spectrum in the large-$N_c$ two-dimensional QCD, known as the 't Hooft model, by addressing the most general case of quarks with unequal masses. Based on our previous work, we develop non-perturbative methods to compute spectral sums and systematically derive large-$n$ WKB expansion of the spectrum. Furthermore, we examine the behavior of these results in various asymptotic regimes, including the chiral, heavy quark, and heavy-light limits, and establish a precise coincidence with known analytical and numerical results obtained through alternative approaches.

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arXiv2023

The eigenvalue spectrum of a large real antisymmetric random matrix with non-zero mean

We study the eigenvalue spectrum of a large real antisymmetric random matrix $J_{ij}$. Using a fermionic approach and replica trick, we obtain a semicircular spectrum of eigenvalues when the mean value of each matrix element is zero, and in the case of a non-zero mean, we show that there is a set of critical finite mean values above which eigenvalues arise that are split off from the semicircular continuum of eigenvalues. The result converged with numerical simulations.

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