arXiv subjects

Viacheslav Krivorol

Publications and source records attributed to Viacheslav Krivorol.

7 recordsLinked to original sources

arXiv2026

Holomorphic Quantization in Constant Curvature Backgrounds

We present a holomorphic quantization scheme for free point particles on two-dimensional constant curvature Riemannian backgrounds. The procedure is based on a Lagrangian embedding of the particle configuration space into a product of coadjoint orbits of the background isometry group. Examples are provided by particles on the plane, torus, sphere, and hyperbolic plane, with or without a monopole field. We elaborate the method by recovering the Hamiltonian spectrum and the wave functions on such spaces. As a by-product, we obtain a geometric and physical interpretation of Repka's result on the decomposition of tensor products of $\mathbf{SL}(2,\mathbb{R})$ discrete series representations.

hep-th↗

arXiv2026

Point Particles as Spin Chains

This work surveys a recently developed approach to the study of free point particles on Riemannian manifolds, based on the Kirillov orbit method, geometric quantization, and the geometry of Lagrangian submanifolds. We discuss that given a Lagrangian submanifold $\mathcal{M}$ embedded in a product of coadjoint orbits and a Hamiltonian $H$ attaining its minimum on this submanifold, such a configuration naturally induces free point particle dynamics on $\mathcal{M}$. The metric governing this dynamics is precisely defined by the quadratic expansion of $H$ around its minimum. Upon quantization, this correspondence establishes a relation between the $L^2(\mathcal{M})$ and a corresponding spin chain Hilbert space as well as a spectral equivalence between Laplace-Beltrami operator on $L^2(\mathcal{M})$ and a spin Hamiltonian. Explicit examples of this construction are presented for particles moving on the complex plane, two-dimensional sphere, flag manifolds, and the hyperbolic plane.

hep-th↗

arXiv2025

On First-Order GLSM for Sigma Models

We review some recent developments in 1-st order GLSM construction, or so-called Gross-Neveu formalism for sigma models. We recall the general idea behind this framework and describe a 1-st order GLSM data from which the general generalized Gross-Neveu model can be constructed, using $\mathbb{CP}^{n-1}$ sigma model as simplest example. Then, we formulate a general statement that answers the question of which generalized Gross-Neveu models are equivalent to sigma models on compact homogeneous Hermitian spaces of classical groups endowed with the normal metrics.

hep-th↗

arXiv2024

Oscillator Calculus on Coadjoint Orbits and Index Theorems

We consider quantum mechanical systems of spin chain type, with finite-dimensional Hilbert spaces and $\mathcal{N}=2$ or $\mathcal{N}=4$ supersymmetry, described in $\mathcal{N}=2$ superspace in terms of nonlinear chiral multiplets. We prove that they are natural truncations of 1D sigma models, whose target spaces are $\mathsf{SU}(n)$ (co)adjoint orbits. As a first application, we compute the Witten indices of these finite-dimensional models showing that they reproduce the Dolbeault and de Rham indices of the target space. The problem of finding the exact spectra of generalized Laplace operators on such orbits is shown to be equivalent to the diagonalization of spin chain Hamiltonians.

hep-th↗

arXiv2024

Supersymmetric Grassmannian Sigma Models in Gross-Neveu Formalism

We revisit the classical aspects of $\mathcal{N}=(2,2)$ supersymmetric sigma models with Hermitian symmetric target spaces, using the so-called Gross-Neveu (first-order GLSM) formalism. We reformulate these models for complex Grassmannians in terms of simple supersymmetric Lagrangians with polynomial interactions. For maximal isotropic Grassmannians we propose two types of equivalent Lagrangians, which make either supersymmetry or the geometry of target space manifest. These reformulations can be seen as current-current deformations of curved $βγ$ systems. The $\mathsf{CP}^{1}$ supersymmetric sigma model is our prototypical example.

hep-th↗

arXiv2023

Grassmannian Sigma Models

We show that sigma models with orthogonal and symplectic Grassmannian target spaces admit chiral Gross-Neveu model formulations, thus extending earlier results on unitary Grassmannians. As a first application, we calculate the one-loop $β$-functions in this formalism, showing that they are proportional to the dual Coxeter numbers of the respective symmetry algebras.

hep-th↗

arXiv2022

Kinetic coefficients in the formalism of time-dependent Green's functions at finite temperature

We discuss the microscopical justification of dissipation in the model nonrelativistic Fermi and Bose systems with weak local interactions above phase transitions. The dynamics of equilibrium fluctuations are considered in Keldysh - Schwinger framework. We show that the dissipation is related to pinch singularities of the diagram technique. Using Dyson - Schwinger equation and the two-loop approximation we define and calculate the attenuation parameter which is related to exponentiality of Green's functions decay. We show that the attenuation parameter is the microscopic analogue of the Onsager kinetic coefficient and it is related to attenuation in the excitation spectrum.

cond-mat.stat-mech↗