Grassmannian Sigma Models

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Grassmannian Sigma Models

Advances in Theoretical and Mathematical Physics. 2024. Vol. 28. No. 3. P. 1027–1079.

Krivorol V., Быков Д. В.

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.

Language: English

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PHYSICS OF ELEMENTARY PARTICLES AND ATOMIC NUCLEI. THEORY

Krivorol V., [б.и.], 2025.

We review some recent developments in 1st order GLSM construction, or so-called Gross–Neveu formalism for sigma models. We recall the general idea behind this framework and describe a 1st order GLSM data from which the general generalized Gross–Neveu model can be constructed, using CP^1 sigma model as simplest example. Then, we formulate a general statement that ...

Added: December 26, 2025

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Krivorol V., Быков Д. В., Letters in Mathematical Physics 2025 Vol. 115 No. 4 Article 85

We revisit the classical aspects of 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 ...

Added: December 26, 2025

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Evgenii Ievlev, Andrei Marshakov, Sumbatian G. et al., Physical Review D - Particles, Fields, Gravitation and Cosmology 2025 Vol. 112 No. 10 Article 105010

It has been shown that the non-Abelian vortex string in 4D N = 2 supersymmetric QCD (SQCD) with the U(2) gauge group and N_f = 4 flavors becomes a critical superstring. Its 10D target space is a product of the flat 4D space and an internal noncompact Calabi-Yau threefold, namely, the conifold. It was also shown that the Coulomb branch ...

Added: December 2, 2025

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Bychkov A., Litvinov A., Journal of High Energy Physics 2025 Vol. 2025 Article 80

In this paper, we explore a new class of integrable sigma models, which we refer to as the “dual regime” of Yang-Baxter (YB) deformed O(2N) sigma models. This dual regime manifests itself in the conformal perturbation approach. Namely, it is well known that conventional YB-deformed O(N) sigma models are described in the UV by a ...

Added: October 13, 2025

Search for NS 3-form flux-induced vacua for the critical non-abelian vortex string

E. Ievlev, Pichugina P., A. Yung, International Journal of Modern Physics A 2025 Vol. 40 No. 24 Article 2550091

It has been demonstrated that the non-Abelian solitonic vortex string in four-dimensional (4D) N=2 supersymmetric QCD (SQCD) with gauge group U(2) and Nf=4 quark hypermultiplets behaves as a critical superstring. This string propagates in a ten-dimensional space comprising the flat 4D space and an internal Calabi–Yau noncompact threefold, specifically, the conifold. The lowest state of this string is a ...

Added: October 2, 2025

2D sigma models on noncompact Calabi-Yau manifolds and Liouville theory

Gavrilenko P., Evgenii Ievlev, Marshakov A. et al., Physical Review D - Particles, Fields, Gravitation and Cosmology 2025 Vol. 111 No. 10 Article 106003

We consider a class of two dimensional conformal N = 2 supersymmetric U(1) gauge linear sigma models with N fields of charges +1 and N fields of charges −1, whose Higgs branches are noncompact toric Calabi-Yau manifolds of complex dimension 2N − 1. We show, starting from large-N approximation, that the Coulomb branch of these models, which opens up at ...

Added: May 14, 2025

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It has been shown that non-Abelian solitonic vortex string supported in four-dimensional (4D) N = 2 supersymmetric QCD (SQCD) with the U(2) gauge group and Nf =4 quark flavors becomes a critical superstring. This string propagates in the ten-dimensional space formed by a product of the flat 4D space and an internal space given by a Calabi-Yau noncompact threefold, ...

Added: September 20, 2024

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Alfimov M., Kalinichenko I., Litvinov A., Journal of High Energy Physics 2024 Vol. 5 Article 297

We study the regularization scheme dependence of Kähler (N=2) supersymmetric sigma models. At the one-loop order the metric beta-function is the same as in the non-supersymmetric case and it coincides with the Ricci tensor. The first correction in the MS scheme is known to appear in the fourth loop. We show that for certain integrable ...

Added: July 16, 2024

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We study effective dynamics of the nonsupersymmetric two-dimensional CP(N-1) model in the large N limit. This model is deformed by a mass term m preserving Z_N symmetry of the Lagrangian. At small m the theory is strongly coupled and resembles the undeformed CP(N-1) model, while at large m it is in a weakly coupled Higgs phase with spontaneously broken Z_N.We ...

Added: May 3, 2024

Peculiarities of beta functions in sigma models

Gamayun O., Losev A. S., Shifman M., Journal of High Energy Physics 2023 No. 10 Article 97

In this paper we consider perturbation theory in generic two-dimensional sigma models in the so-called first-order formalism, using the coordinate regularization approach. Our goal is to analyze the first-order formalism in application to β functions and compare its results with the standard geometric calculations. Already in the second loop, we observe deviations from the geometric results that ...

Added: November 10, 2023

NS three-form flux deformation for the critical non-Abelian vortex string

A. Yung, Physical Review D - Particles, Fields, Gravitation and Cosmology 2022 Vol. 106 No. 10 Article 106019

It has been shown that the non-Abelian solitonic vortex string supported in four-dimensional (4D) N = 2 supersymmetric QCD (SQCD) with the U(2) gauge group and N_f = 4 quark flavors becomes a critical superstring. This string propagates in the ten-dimensional space formed by a product of the flat 4D space and an internal space given by a Calabi-Yau noncompact ...

Added: December 21, 2022

Dynamics of non-Abelian strings in the theory interpolating from N=2 to N=1 supersymmetric QCD

Gorsky A., E. Ievlev, A. Yung, Physical Review D - Particles, Fields, Gravitation and Cosmology 2020 Vol. 101 No. 1 Article 014013

We study the dynamics of non-Abelian vortex strings supported in N =2 supersymmetric QCD with the U(N) gauge group and N_f = N quark flavors deformed by the mass μ of the adjoint matter. In the limit of large μ the bulk four-dimensional theory flows to N = 1 supersymmetric QCD. The dynamics of orientational zero modes of the non-Abelian string ...

Added: October 31, 2022

Long Way to Ricci Flatness

Chen J., Sheu C., Shifman M. et al., Journal of High Energy Physics 2020 Vol. 2020 No. 10 Article 59

We study two-dimensional weighted N = (2; 2) supersymmetric CP models with the goal of exploring their infrared (IR) limit. WCP(N, tildeN) are simplifed versions of world-sheet theories on non-Abelian strings in four-dimensional N = 2 QCD. In the gauged linear sigma model (GLSM) formulation, WCP(N, tildeN) has N charges +1 and tilde N charges -1 fields. As well-known, at e N ...

Added: October 31, 2022

String baryon in four-dimensional N=2 supersymmetric QCD from the 2D-4D correspondence

E. Ievlev, Shifman M., A. Yung, Physical Review D - Particles, Fields, Gravitation and Cosmology 2020 Vol. 102 No. 5 Article 054026

We study non-Abelian vortex strings in four-dimensional (4D) N = 2 supersymmetric QCD with the U(2) gauge group and N_f =4 flavors of quark hypermultiplets. It has recently been shown that these vortices behave as critical superstrings. The spectrum of closed string states in the associated string theory was found and interpreted as a spectrum of hadrons in 4D N ...

Added: October 31, 2022

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S. Derkachov, Isaev A. P., Shumilov L., Physics Letters B 2022 Vol. 830 Article 137150

A convenient operator representation for zig-zag four-point and two-point planar Feynman diagrams relevant to the bi-scalar D-dimensional “fishnet” field theory is obtained. This representation gives a possibility to evaluate exactly diagrams of the zig-zag series in special cases. In particular, we give a fairly simple proof of the Broadhurst-Kreimer conjecture about the values of zig-zag multi-loop two-point diagrams ...

Added: October 27, 2022

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It has been shown that non-Abelian vortex string supported in four-dimensional (4D) N =2 supersymmetric QCD (SQCD) with the U(2) gauge group and N_f =4 quark flavors becomes a critical superstring. This string propagates in the ten-dimensional space formed by a product of the flat 4D space and an internal space given by a Calabi-Yau noncompact threefold, namely, ...

Added: October 26, 2022

The Canonical Operator in Many-Particle Problems and Quantum Field Theory

Maslov, Victor P., Shvedov O., De Gruyter, 2022.

In this monograph we study the problem of construction of asymptotic solutions of equations for functions whose number of arguments tends to infinity as the small parameter tends to zero. Such equations arise in statistical physics and in quantum theory of a large number of fi elds. We consider the problem of renormalization of quantum ...

Added: July 1, 2022