Related papers: Homogeneous Yang-Baxter deformations as generalize…
We propose a generalisation of the notion of associated bundles to a principal bundle constructed via group action cocycles rather than via mere representations of the structure group. We devise a notion of connection generalising Ehresmann…
A dual weak brace is an algebraic structure $\left(S,\,+,\,\circ\right)$ including skew braces and giving rise to a set-theoretic solution of the Yang-Baxter equation. We show that such a map belongs to a family of set-theoretic solutions,…
This is a sequel of our paper hep-th/0606125 in which we have studied the {\cal N}=1 SU(N) SYM theory obtained as a marginal deformation of the {\cal N}=4 theory, with a complex deformation parameter \beta and in the planar limit. There we…
We consider supersymmetric deformations of gauge theories in various dimensions obtained from a String Theory realisation of branes embedded in flux backgrounds. In particular we obtain deformations which take the form of Wilson line…
We associate a deformation of Heisenberg algebra to the suitably normalized Yang $R$-matrix and we investigate its properties. Moreover, we construct new examples of quantum vertex algebras which possess the same representation theory as…
N=4 supersymmetric Yang-Mills theory with gauge group SU(n) (n>=3) is believed to have two exactly marginal deformations which break the supersymmetry to N=1. We discuss the construction of the string theory dual to these deformations, in…
In this paper, we introduce and investigate a general transformation or change of Finsler metrics, which is referred to as a generalized $\beta$-conformal change: $$L(x,y) \longrightarrow\overline{L}(x,y) =…
It has recently been shown that a set of the generalized type IIB supergravity equations follows from the requirement of kappa symmetry of the type IIB Green-Schwarz superstring theory defined on an arbitrary background. In this paper, we…
An operator deformed quantum algebra is discovered exploiting the quantum Yang-Baxter equation with trigonometric R-matrix. This novel Hopf algebra along with its $q \to 1$ limit appear to be the most general Yang-Baxter algebra underlying…
A new method for obtaining dual string theory backgrounds is presented. Preservation of the Hamiltonian density and the energy momentum tensor induced by O(d,d)-transformations leads to a relation between dual sets of coordinate one-forms…
We construct supergravity backgrounds for the integrable eta-deformations of the AdS2 x S2 x T6 and AdS5 x S5 superstring sigma models. The eta-deformation is governed by an R-matrix that solves the non-split modified classical Yang-Baxter…
A common approach to the quantization of integrable models starts with the formal substitution of the Yang-Baxter Poisson algebra with its quantum version. However it is difficult to discern the presence of such an algebra for the so-called…
Baxter operators are constructed for quantum spin chains with deformed $s\ell_2$ symmetry. The parallel treatment of Yang-Baxter operators for the cases of undeformed, trigonometrically and elliptically deformed symmetries presented earlier…
By calculating inequivalent classical r-matrices for the $gl(2,\mathbb{R})$ Lie algebra as solutions of (modified) classical Yang-Baxter equation ((m)CYBE)), we classify the YB deformations of Wess-Zumino-Witten (WZW) model on the…
Starting with exact solutions to string theory on curved spacetimes we obtain deformations that represent gravitational shock waves. These may exist in the presence or absence of sources. Sources are effectively induced by a tachyon field…
This is an introduction to an algebraic construction of a gravity theory on noncommutative spaces which is based on a deformed algebra of (infinitesimal) diffeomorphisms. We start with some fundamental ideas and concepts of noncommutative…
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 present a systematic procedure to obtain singular solutions of the constant quantum Yang-Baxter equation in arbitrary dimension. This approach, inspired in the Lie (super)algebra structure, is explicitly applied to the particular case of…
We consider generalizations of the Snyder algebra to a curved spacetime background with de Sitter symmetry. As special cases, we obtain the algebras of the Yang model and of triply special relativity. We discuss the realizations of these…
We introduce a cohomology theory of $n$-ary self-distributive objects in the tensor category of vector spaces that classifies their infinitesimal deformations. For $n$-ary self-distributive objects obtained from $n$-Lie algebras we show…