English
Related papers

Related papers: On exactly solvable Yang-Baxter models and enhance…

200 papers

Supersymmetry algebras can be used to obtain algebraic expressions for constant Yang-Baxter solutions, also known as braid group generators. This was done for non-invertible braid operators in \cite{maity2025non}. In this work we extend…

High Energy Physics - Theory · Physics 2025-08-07 Somnath Maity , Pramod Padmanabhan , Jarmo Hietarinta , Vladimir Korepin

It is known that the supermultiplet of beta-deformations of ${\cal N}=4$ supersymmetric Yang-Mills theory can be described in terms of the exterior product of two adjoint representations of the superconformal algebra. We present a…

High Energy Physics - Theory · Physics 2018-11-12 Andrei Mikhailov , Segundo P. Milián

The maximally supersymmetric Yang-Mills theory in four-dimensional Minkowski space is an exceptional model of mathematical physics. Even more so in the planar limit, where the theory is believed to be integrable. In particular, the…

High Energy Physics - Theory · Physics 2018-11-16 Nils Kanning

We prove, using the coordinate Bethe ansatz, the exact solvability of a model of three particles whose point-like interactions are determined by the root system of g_2. The statistics of the wavefunction are left unspecified. Using the…

Mathematical Physics · Physics 2007-05-23 N. Crampe , C. A. S. Young

We show that twisted reduced models can be interpreted as noncommutative Yang-Mills theory. Based upon this correspondence, we obtain noncommutative Yang-Mills theory with D-brane backgrounds in IIB matrix model. We propose that IIB matrix…

High Energy Physics - Theory · Physics 2009-10-31 H. Aoki , N. Ishibashi , S. Iso , H. Kawai , Y. Kitazawa , T. Tada

We study integrable deformations of two-dimensional non-linear sigma-models and present a new class of classical solutions to critical bi-Yang-Baxter models for general groups. For the simplest example, namely the SL(2,R) bi-Yang-Baxter…

High Energy Physics - Theory · Physics 2022-12-09 Thomas W. Grimm , Jeroen Monnee

We study the null dipole deformation of N=4 super Yang-Mills theory, which is an example of a potentially solvable "dipole CFT": a theory that is non-local along a null direction, has non-relativistic conformal invariance along the…

High Energy Physics - Theory · Physics 2019-02-01 Monica Guica , Fedor Levkovich-Maslyuk , Konstantin Zarembo

Connections between set-theoretic Yang-Baxter and reflection equations and quantum integrable systems are investigated. We show that set-theoretic $R$-matrices are expressed as twists of known solutions. We then focus on reflection and…

Mathematical Physics · Physics 2021-08-10 Anastasia Doikou , Agata Smoktunowicz

We propose a generic framework to obtain certain types of contracted and centrally extended algebras. This is based on the existence of quadratic algebras (reflection algebras and twisted Yangians), naturally arising in the context of…

High Energy Physics - Theory · Physics 2009-11-13 Anastasia Doikou , Konstadinos Sfetsos

We construct the Lax-pair, the classical monodromy matrix and the corresponding solution of the Yang--Baxter equation, for a two-parameter deformation of the Principal chiral model for a simple group. This deformation includes as a…

High Energy Physics - Theory · Physics 2014-12-30 Georgios Itsios , Konstantinos Sfetsos , Konstantinos Siampos , Alessandro Torrielli

In this paper we discuss and characterize several set-theoretic solutions of the Yang-Baxter equation obtained using skew lattices, an algebraic structure that has not yet been related to the Yang-Baxter equation. Such solutions are…

Quantum Algebra · Mathematics 2020-02-06 Karin Cvetko-Vah , Charlotte Verwimp

Several years ago, it was proposed that the usual solutions of the Yang-Baxter equation associated to Lie groups can be deduced in a systematic way from four-dimensional gauge theory. In the present paper, we extend this picture, fill in…

High Energy Physics - Theory · Physics 2019-04-23 Kevin Costello , Edward Witten , Masahito Yamazaki

Recently, researchers have proposed the Asymmetric Bethe ansatz method - a theoretical tool that extends the scope of Bethe ansatz-solvable models by "breaking" partial mirror symmetry via the introduction of a fully reflecting boundary.…

Exactly Solvable and Integrable Systems · Physics 2026-01-21 Wen-Jie Qiu , Xi-Wen Guan , Yi-Cong Yu

Applying braided Yang-Baxter equation quantum integrable and Bethe ansatz solvable 1D anyonic lattice and field models are constructed. Along with known models we discover novel lattice anyonic and $q$-anyonic models as well as nonlinear…

Exactly Solvable and Integrable Systems · Physics 2015-02-04 Anjan Kundu

The Yang-Baxter (YB) deformations of Wess-Zumino-Witten (WZW) model on the Heisenberg Lie group ($H_4$) are examined. We proceed to obtain the nonequivalent solutions of (modified) classical Yang-Baxter equation ((m)CYBE) for the $ h_4$ Lie…

High Energy Physics - Theory · Physics 2021-05-04 Ali Eghbali , Tayebe Parvizi , Adel Rezaei-Aghdam

Planar N=4 super Yang-Mills appears to be integrable. While this allows to find this theory's exact spectrum, integrability has hitherto been of no direct use for scattering amplitudes. To remedy this, we deform all scattering amplitudes by…

High Energy Physics - Theory · Physics 2013-03-27 Livia Ferro , Tomasz Lukowski , Carlo Meneghelli , Jan Plefka , Matthias Staudacher

It is shown that square free set theoretic involutive non-degenerate solutions of the Yang-Baxter equation whose associated permutation group (referred to as an involutive Yang-Baxter group) is abelian are retractable in the sense of…

Group Theory · Mathematics 2009-03-23 Ferran Cedo , Eric Jespers , Jan Okninski

We study the deformation theory of the Einstein-Yang-Mills system on a principal bundle with a compact structure group over a compact manifold. We first construct, as an application of the general slice theorem of Diez and Rudolph, a smooth…

Differential Geometry · Mathematics 2025-07-18 Severin Bunk , Vicente Muñoz , C. S. Shahbazi

The theory of the set-theoretic Yang-Baxter equation is reviewed from a purely algebraic point of view. We recall certain algebraic structures called shelves, racks and quandles. These objects satisfy a self-distributivity condition and…

Mathematical Physics · Physics 2026-02-24 Anastasia Doikou

Given an associative multiplication in matrix algebra compatible with the usual one or, in other words, linear deformation of matrix algebra, we construct a solution to the classical Yang-Baxter equation. We also develop a theory of such…

Quantum Algebra · Mathematics 2007-05-23 Alexander Odesskii , Vladimir Sokolov