English
Related papers

Related papers: Structure of the string R-matrix

200 papers

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

For any algebra two families of coloured Yang-Baxter operators are constructed, thus producing solutions to the two-parameter quantum Yang-Baxter equation. An open problem about a system of functional equations is stated. The matrix forms…

Quantum Algebra · Mathematics 2007-05-23 Florin F. Nichita , Deepak Parashar

The theory of the parametric set-theoretic Yang-Baxter equation is established from a purely algebraic point of view. The first step towards this objective is the introduction of certain generalizations of the familiar shelves and racks…

Mathematical Physics · Physics 2026-02-10 Anastasia Doikou

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

The deformed algebra $\cal{A(R)}$, depending upon a Yang-Baxter R- matrix, is considered. The conditions under which the algebra is associative are discussed for a general number of oscillators. Four types of solutions satisfying these…

High Energy Physics - Theory · Physics 2019-08-17 S. Meljanac , M. Milekovic , A. Perica

We explore the algebraic structure of a particular ansatz of Yang Baxter Equation which is inspired from the Bethe Ansatz treatment of the ASEP spin-model. Various classes of Hamiltonian density arriving from two types of R-Matrices are…

Statistical Mechanics · Physics 2024-11-19 Suvendu Barik , Alexander. S. Garkun , Vladimir Gritsev

We introduce the special set-theoretic Yang-Baxter algebra and show that it is a Hopf algebra subject to certain conditions. The associated universal R-matrix is also obtained via an admissible Drinfel'd twist. The structure of braces…

Quantum Algebra · Mathematics 2025-11-18 Anastasia Doikou

Quantization of two-dimensional Yang-Mills theory on a torus in the gauge where the field strength is diagonal leads to twisted sectors that are completely analogous to the ones that originate long string states in Matrix String Theory. If…

High Energy Physics - Theory · Physics 2009-10-31 M. Billo' , M. Caselle , A. D'Adda , P. Provero

Recently V.Drinfeld formulated a number of problems in quantum group theory. In particular, he suggested to consider ``set-theoretical'' solutions of the quantum Yang-Baxter equation, i.e. solutions given by a permutation $R$ of the set…

q-alg · Mathematics 2008-02-03 Pavel Etingof , Travis Schedler , Alexandre Soloviev

In this note we give an explicit formula for the preserved Killing spinors in deformed string theory backgrounds corresponding to integrable Yang--Baxter deformations realized via (sequences of) TsT transformations. The Killing spinors can…

High Energy Physics - Theory · Physics 2019-09-04 Domenico Orlando , Susanne Reffert , Yuta Sekiguchi , Kentaroh Yoshida

We construct type $g\ell(n)$ Yangian algebra evaluations of order $N$ embedded in Heisenberg algebras and consider their representations having a highest weight. These Yangian algebra presentations depend on $nN$ parameters. We construct…

Quantum Algebra · Mathematics 2025-08-19 R. Kirschner

This work is based on the author's PhD thesis. The main result of the thesis is the use of the boost operator to develop a systematic method to construct new integrable spin chains with nearest-neighbour interaction and characterized by an…

Statistical Mechanics · Physics 2023-12-04 Chiara Paletta

The gauge symmetries that underlie string theory arise from inner automorphisms of the algebra of observables of the associated conformal field theory. In this way it is possible to study broken and unbroken symmetries on the same footing,…

High Energy Physics - Theory · Physics 2015-06-26 Mark Evans , Ioannis Giannakis

In this paper we review the theory of the Yang-Baxter equation related to the 6-vertex model and its higher spin generalizations. We employ a 3D approach to the problem. Starting with the 3D R-matrix, we consider a two-layer projection of…

Mathematical Physics · Physics 2014-06-11 Vladimir V. Mangazeev

We exploit a conjectured continuity between super Yang-Mills on $\mathbb R^3\times \mathbb S^1$ and pure Yang-Mills to study $k$-strings in the latter theory. As expected, we find that Wilson-loop correlation functions depend on the N-ality…

High Energy Physics - Theory · Physics 2018-01-01 Mohamed M. Anber , Vito Pellizzani

It is known that integrable models associated to rational $R$ matrices give rise to certain non-abelian symmetries known as Yangians. Analogously `boundary' symmetries arise when general but still integrable boundary conditions are…

High Energy Physics - Theory · Physics 2010-11-24 Anastasia Doikou

We study the Yangians Y(a) associated with the simple Lie algebras a of type B, C or D. The algebra Y(a) can be regarded as a quotient of the extended Yangian X(a) whose defining relations are written in an R-matrix form. In this paper we…

Quantum Algebra · Mathematics 2009-11-11 D. Arnaudon , A. Molev , E. Ragoucy

The analytic structure of the S-matrix of singular quantum mechanics is examined within a multichannel framework, with primary focus on its dependence with respect to a parameter ($\Omega$) that determines the boundary conditions.…

Quantum Physics · Physics 2015-06-15 Horacio E. Camblong , Luis N. Epele , Huner Fanchiotti , Carlos A. Garcia Canal

This is a review article in which we will introduce, in a unifying fashion and with more intermediate steps in some difficult calculations, two infinite-dimensional Lie algebras of quantum matrix models, one for the open string sector and…

High Energy Physics - Theory · Physics 2009-10-31 C. -W. H. Lee , S. G. Rajeev

Orthogonal or symplectic Yangians are defined by the Yang-Baxter $RLL$ relation involving the fundamental $R$ matrix with $so(n)$ or $sp(2m)$ symmetry. Simple $L$ operators with linear or quadratic dependence on the spectral parameter exist…

Mathematical Physics · Physics 2018-08-01 D. Karakhanyan , R. Kirschner