Related papers: On exactly solvable Yang-Baxter models and enhance…
We discuss infinite-dimensional hidden symmetry algebras (and hence an infinite number of conserved nonlocal charges) of the N-extented self-dual super Yang-Mills equations for general N\leq4 by using the supertwistor correspondence.…
In this article, we reconsider the formulation of Yangian symmetry for planar N=4 supersymmetric Yang-Mills theory, and we investigate to what extent this symmetry lifts to the beta/gamma-deformation of the model. We first apply cohomology…
In the classification of solutions of the Yang--Baxter equation, there are solutions that are not deformations of the trivial solution (essentially the identity). We consider the algebras defined by these solutions, and the corresponding…
We explore a deformation of the flat space symmetric space sigma model action. The deformed action is designed to allow a Lax connection for the equations of motion, similar to the undeformed model. For this to work, we identify a set of…
We continue to explore the previously suggested dual regime of Yang-Baxter (YB) deformed $\mathrm{O}(2N)$ sigma models, which is a new one-parametric deformation of the $\mathrm{O}(2N)$ model. It can be obtained from the conventional YB…
We examine classes of quantum algebras emerging from involutive, non-degenerate set-theoretic solutions of the Yang-Baxter equation and their q-analogues. After providing some universal results on quasi-bialgebras and admissible Drinfeld…
We show how any integrable 2D QFT enjoys the existence of infinitely many non--abelian {\it conserved} charges satisfying a Yang--Baxter symmetry algebra. These charges are generated by quantum monodromy operators and provide a…
A new class of completely integrable models is constructed. These models are deformations of the famous integrable and exactly solvable Gaudin models. In contrast with the latter, they are quasi-exactly solvable, i.e. admit the algebraic…
A lattice regularized Lax operator for the nonultralocal modified Korteweg de Vries (mKdV) equation is proposed at the quantum level with the basic operators satisfying a $q$-deformed braided algebra. Finding further the associated quantum…
We study integrable models in the context of the recently discovered Gauge/YBE correspondence, where the Yang-Baxter equation is promoted to a duality between two supersymmetric gauge theories. We study flavored elliptic genus of 2d…
Marginal beta deformations of N=4 super-Yang-Mills theory are known to correspond to a certain class of deformations of the S^5 background subspace of type IIB string theory in AdS_5 x S^5. An analogous set of deformations of the AdS_5…
We study simple set-theoretic solutions of the Yang-Baxter equation that are finite and non-degenerate. Such retractable solutions are fully described and to investigate the irretracble solutions we give a new algebraic method. Our approach…
Two-dimensional $\sigma$-models with $\mathbb{Z}_N$-symmetric homogeneous target spaces have been shown to be classically integrable when introducing WZ-terms in a particular way. This article continues the search for new models of this…
We work towards the classification of all one-dimensional exclusion processes with two species of particles that can be solved by a nested coordinate Bethe Ansatz. Using the Yang-Baxter equations, we obtain conditions on the model…
We describe several methods of constructing R-matrices that are dependent upon many parameters, for example unitary R-matrices and R-matrices whose entries are functions. As an application, we construct examples of R-matrices with…
A large class of the recently found unimodular nonabelian homogeneous Yang-Baxter deformations of the AdS_5 x S^5 superstring can be realized as sequences of noncommuting TsT transformations. I show that many of them are duals to various…
In the first part of this paper, we investigate the retraction of finite uniconnected involutive non-degenerate set-theoretic solutions of the Yang-Baxter equation by means of left braces, giving a precise description in some cases. In the…
Set-theoretic solutions of the Yang--Baxter equation form a meeting-ground of mathematical physics, algebra and combinatorics. Such a solution consists of a set $X$ and a function r:X x X --> X x X which satisfies the braid relation. We…
We demonstrate that the planar real-$\beta$-deformed Super-Yang--Mills theory possesses an infinitely-dimensional Yangian symmetry algebra and thus is classically integrable. This is achieved by the introduction of the twisted coproduct…
The spectral decomposition of regular Uq(sl_2)-invariant solutions of the Yang-Baxter equation is studied. An algorithm for finding all possible solutions of spin s is developed. It also allows to reconstruct the R-matrix from a given…