Related papers: Yang-Baxter deformations of the flat space string

In this article, we introduce endocabling as a technique to deform involutive, non-degenerate set-theoretic solutions to the Yang-Baxter equation (``solutions'', for short) by means of $\lambda$-endomorphisms of their associated permutation…

We propose a method for constructing the Lax connection of two-dimensional relativistic integrable sigma models on coset spaces by means of exponentiation of a suitable operator. We derive a simple quadratic relation that this operator must…

The quantum Yang-Baxter equation is a braiding condition on vector spaces which is of high relevance in several fields of mathematics, such as knot theory and quantum group theory. Their combinatorial counterpart are set-theoretic solutions…

Classical Yang-Baxter equation governing bi-vector deformations of 10d supergravity is known to have no solutions along non-abelian compact isometries. By providing explicit examples we show that this is in contrast to generalized…

We consider involutive, non-degenerate, finite set theoretic solutions of the Yang-Baxter equation. Such solutions can be always obtained using certain algebraic structures that generalize nil potent rings called braces. Our main aim here…

Inspired by the work of Wang and Zhou [4] for Rota-Baxter algebras, we develop a cohomology theory of Rota-Baxter systems and justify it by interpreting the lower degree cohomology groups as formal deformations and as abelian extensions of…

We introduce non-degenerate solutions of the Yang-Baxter equation in the setting of symmetric monoidal categories. Our theory includes non-degenerate set-theoretical solutions as basic examples. However, infinite families of non-degenerate…

In this short article we develop recent proposals to relate Yang-Baxter sigma-models and non-abelian T-duality. We demonstrate explicitly that the holographic space-times associated to both (multi-parameter)-$\beta$-deformations and…

We explore two distinct methods to introduce integrable defects in a family of integrable sigma-models known as Yang-Baxter models. The first method invokes a modified monodromy matrix encoding an integrable defect separating two integrable…

A completely integrable dynamical system in discrete time is studied by means of algebraic geometry. The system is associated with factorization of a linear operator acting in a direct sum of three linear spaces into a product of three…

We show that B-type $\Pi$-stable D-branes do not in general reduce to the (Gieseker-) stable holomorphic vector bundles used in mathematics to construct moduli spaces. We show that solutions of the almost Hermitian Yang--Mills equations for…

In the absence of NSNS three-form flux the bosonic string on a symmetric space is described by a symmetric space coset sigma-model. Such models are known to be classically integrable. We show that the integrability extends also to cases…

We study the interplay between a particular marginal deformation of ${\cal N}=4$ super Yang-Mills theory, the $\beta$ deformation, and integrability in the holographic setting. Using modern methods of analytic non-integrability of…

Let $r:X^{2}\rightarrow X^{2}$ be a set-theoretic solution of the Yang-Baxter equation on a finite set $X$. It was proven by Gateva-Ivanova and Van den Bergh that if $r$ is non-degenerate and involutive then the algebra $K\langle x \in X…

It is shown that dimers is Yang-Baxter integrable as a six-vertex model at the free-fermion point with crossing parameter $\lambda=\tfrac{\pi}{2}$. A one-to-many mapping of vertex onto dimer configurations allows the free-fermion solutions…

Let $\Sigma$ be a closed surface, $G$ a compact Lie group, not necessarily connected, with Lie algebra $g$, endowed with an adjoint action invariant scalar product, let $\xi \colon P \to \Sigma$ be a principal $G$-bundle, and pick a…

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…

In this paper, we establish the cohomology of relative Rota-Baxter operators on Lie-Yamaguti algebras via the Yamaguti cohomology. Then we use this type of cohomology to characterize deformations of relative Rota-Baxter operators on…

In this note we study `a la Baxter [1] the possible integrable manifolds of the asymmetric eight-vertex model. As expected they occur when the Boltzmann weights are either symmetric or satisfy the free-fermion condition but our analysis…

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…