20 pages. Covariant expression of the corrections improved. Comments on tests added. Concluding comments expanded. References added, and other minor changes. Published version
We use the $O(d,d)$-covariant formulation of supergravity familiar from Double Field Theory to find the first $α'$-correction to (unimodular) homogeneous Yang-Baxter (YB) deformations of the bosonic string. A special case of this result gives the $α'$-correction to TsT transformations. In a suitable scheme the correction comes entirely from an induced anomalous double Lorentz transformation, which is needed to make the two vielbeins obtained upon the YB deformation equal. This should hold more generally, in particular for abelian and non-abelian T-duality, as we discuss.
The BCFW recursion relation in $\mathcal{N}=4$ super-Yang-Mills theory is solved using Yang-Baxter $R$-operators in the NMHV sector. Explicit expressions for $\mathcal{R}$-invariants are obtained in terms of the chains of $R$-operators acting on an appropriate basic state.
Institute for Information Transmission Problems（信息传输问题研究所）；Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research（杜布纳联合核子研究所玻戈留博夫理论物理实验室）；Moscow Institute of Physics and Technology, Laboratory of High Energy Physics（莫斯科物理技术学院高能物理实验室）
We consider three-parameter Yang-Baxter deformations of the $AdS_5\times T^{1,1}$ superstring for abelian $r$-matrices which are solutions of the classical Yang-Baxter equation. We find two new backgrounds which are dual to the dipole deformed Klebanov-Witten gauge theory and to the nonrelativistic Klebanov-Witten gauge theory with Schrödinger symmetry
We present homogeneous Yang-Baxter deformations of the AdS$_5\times$S$^5$ supercoset sigma model as boundary conditions of a 4D Chern-Simons theory. We first generalize the procedure for the 2D principal chiral model developed by Delduc et al [arXiv:1909.13824] so as to reproduce the 2D symmetric coset sigma model, and specify boundary conditions governing homogeneous Yang-Baxter deformations. Then the conditions are applicable for the AdS$_5\times$S$^5$ supercoset sigma model case as well. In addition, homogeneous bi-Yang-Baxter deformation is also discussed.
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 systems. As an example we construct integrable defects in the ultralocal version of the $S^2$ Yang-Baxter model or 2d Fateev sausage model. The second method is based on the so-called "frozen" Bäcklund transformations. Lifting the construction to the Drinfel'd double, we show how defect matrices can be constructed for inhomogeneous Yang-Baxter models. We pr…
Integrable sigma model with generalized $\mathcal{F}$ structure, Yang-Baxter sigma model with generalized complex structure and multi-Yang-Baxter sigma model
An elliptic Bailey lemma is formulated on the basis of the univariate rarefied elliptic beta integral. It leads to a generalized operator star-triangle relation and a new solution of the Yang-Baxter equation written as an integral operator with a rarefied elliptic hypergeometric kernel.
We introduce an odd supersymmetric version of the Kronecker elliptic function. It satisfies the genus one Fay identity and supersymmetric version of the heat equation. As an application we construct an odd supersymmetric extensions of the elliptic $R$-matrices, which satisfy the classical and the associative Yang-Baxter equations.
