Related papers: Yang-Baxter Deformations Beyond Coset Spaces (a sl…
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…
It is demonstrated how chains of twists for classical Lie algebras induce the new twist deformations (the deformed Yangians) that quantize the generalized rational solutions of the classical Yang-Baxter equation. For the case of Y(g) with…
We use the $O(d,d)$-covariant formulation of supergravity familiar from Double Field Theory to find the first $\alpha'$-correction to (unimodular) homogeneous Yang-Baxter (YB) deformations of the bosonic string. A special case of this…
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…
Linearized solutions of SUGRA equations of motion are described in the pure spinor formalism by vertex operators. Under supersymmetry transformations, they transform covariantly only up to BRST exact terms. We identify the cohomology class…
In this thesis, two aspects of string theory are discussed, tensionless strings and supersymmetric sigma models. The equivalent to a massless particle in string theory is a tensionless string. Even almost 30 years after it was first…
We consider theories with degenerate kinetic terms such as those that arise at strong coupling in $N=2$ super Yang-Mills theory. We compute the components of generalized $N=1,2$ supersymmetric sigma model actions in two dimensions. The…
We introduce a new variety of set-theoretic non-associative algebras, P{\l}onka bi-magmas, to describe and classify all solutions of the set-theoretic Yang-Baxter (YB) equation of Baaj-Long-Skandalis (BLS) type. We also study new classes of…
In this paper a class of new quantum groups is presented: deformed Yangians. They arise from rational solutions of the classical Yang-Baxter equation of the form $c_2 /u + const$ . The universal quantum $R$-matrix for a deformed Yangian is…
We study a Jordanian deformation of the $AdS_5 \times S^5$ superstring that preserves 12 superisometries. It is an example of homogeneous Yang-Baxter deformations, a class that generalises TsT deformations to the non-abelian case. Many of…
This paper investigates Rota-Baxter systems in the sense of Brzezi\'nski from the perspective of operad theory. The minimal model of the Rota-Baxter system operad is constructed, equivalently a concrete construction of its Koszul dual…
A two-dimensional topological sigma-model on a generalized Calabi-Yau target space $X$ is defined. The model is constructed in Batalin-Vilkovisky formalism using only a generalized complex structure $J$ and a pure spinor $\rho$ on $X$. In…
In {\it Set-theoretical solutions to the quantum Yang-Baxter equation} (Duke Math. J. {\bf 100} (1999), 169--209), Etingof, Schedler and Soloviev introduced, for each non-degenerate involutive set-theoretical solution $(X,\sigma,\tau)$ of…
The $\gamma_i$-deformed $\mathcal{N}=4$ super-Yang-Mills theory is a non-supersymmetric deformation of the maximally-supersymmetric gauge theory in four dimensions which is conformally-invariant at the planar level. At the non-planar level…
Rota-Baxter operators and bialgebras are closely connected in several applications, such as the Connes-Kreimer renormalization framework and the operator approach to the classical Yang-Baxter equation. The concept of a Rota-Baxter system…
An ansatz is presented for a possible non-associative deformation of the standard Yang-Mills type gauge theories. An explicit algebraic structure for the deformed gauge symmetry is put forward and the resulting gauge theory developed. The…
The world-sheet S-matrix of the string in AdS5 x S5 has been shown to admit a q-deformation that relates it to the S-matrix of a generalization of the sine-Gordon theory, which arises as the Pohlmeyer reduction of the superstring. Whilst…
Several aspects of relations between braces and non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation are discussed and many consequences are derived. In particular, for each positive integer $n$ a finite square-free…
Given a skew left brace $B$, a method is given to construct all the non-degenerate set-theoretic solutions $(X,r)$ of the Yang Baxter equation such that the associated permutation group $\mathcal{G}(X,r)$ is isomorphic, as a skew left…
Within the framework of the flux formulation of Double Field Theory (DFT) we employ a generalised Scherk-Schwarz ansatz and discuss the classification of the twists that in the presence of the strong constraint give rise to constant…