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Supersymmetric Grassmannian sigma models in Gross–Neveu formalism
Letters in Mathematical Physics. 2025. Vol. 115. No. 4. Article 85.
Krivorol V., Быков Д. В.
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
Krivorol V., Быков Д. В., Advances in Theoretical and Mathematical Physics 2024 Vol. 28 No. 3 P. 1027–1079
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. ...
Added: December 26, 2025
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
Bychkov A., Nekrasov B., Physical Review D - Particles, Fields, Gravitation and Cosmology 2026 Vol. 113 No. 6 Article 066007
We continue to explore the previously suggested dual regime of Yang-Baxter (YB) deformed $\OO(2N)$ sigma models, which is a new one-parametric deformation of the $\OO(2N)$ model. It can be obtained from the conventional YB deformed $\OO(2N+2)$ sigma model by freezing two isometries. The scattering matrix in the non-deformed $\OO(n)$ model is known coincide with the ...
Added: October 14, 2025
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
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
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
A. Yung, Physical Review D - Particles, Fields, Gravitation and Cosmology 2024 Vol. 110 No. 2 Article 025004
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
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
E. Ievlev, Sumbatian G., A. Yung, Physical Review D - Particles, Fields, Gravitation and Cosmology 2024 Vol. 109 No. 8 Article 085021
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
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
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
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
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
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
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
E. Ievlev, A. Yung, Physical Review D - Particles, Fields, Gravitation and Cosmology 2021 Vol. 104 No. 11 Article 114033
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
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