Related papers: Unimodular jordanian deformations of integrable su…
The paper is devoted to the description of the varieties of complex 5-dimensional nilpotent Jordan superalgebras. We find all representatives for the isomorphism classes, using the Jordan normal form, results of simultaneous matrix…
The recently proposed jordanian quantization of the Lie superalgebra $osp(1|2)$ due to the embedding $sl(2) \subset osp(1|2)$, is extended including odd generators into the twisting element $\cal F$. This deformation is obtained as a…
Using deformation theory based on BRST cohomology, a supergravity model is constructed which interpolates through a continuous deformation parameter between new minimal supergravity with an extra U(1) gauge multiplet and standard…
It is shown that the O(d,d;R) deformations of the superstring vacua and the O(d,d+16;R) deformations of the heterotic string vacua preserve extended worldsheet supersymmetry and, hence, generate superconformal deformations. The…
We study triples of graded rings defined over the deformation spaces for certain one-parameter families of Calabi-Yau threefolds. These rings are analogues of the rings of modular forms, quasi-modular forms and almost-holomorphic modular…
In this paper we propose a resolution to the problem of $\beta$-deforming the non-Gaussian monomial matrix models. The naive guess of substituting Schur polynomials with Jack polynomials does not work in that case, therefore, we are forced…
A three-parametric $R$-matrix satisfying a graded Yang-Baxter equation is introduced.This $R$-matrix allows us to construct new quantum supergroups which are deformations of the supergroup $GL(1/1)$ and the universal enveloping algebra…
We study the holographic duals of type II and heterotic matrix string theories described by warped AdS_3 supergravities. By explicitly solving the linearized equations of motion around near horizon D-string geometries, we determine the…
We derive the part of the Lagrangian for the sigma model on the eta-deformed AdS_5 x S^5 space which is quadratic in fermions and has the full dependence on bosons. We then show that there exists a field redefinition which brings the…
The integrable structure of the one-dimensional Hubbard model is based on Shastry's R-matrix and the Yangian of a centrally extended sl(2|2) superalgebra. Alcaraz and Bariev have shown that the model admits an integrable deformation whose…
Recently, a class of transformations of $R_q$-matrices was introduced such that the $q \to 1$ limit gives explicit nonstandard $R_h$-matrices. The transformation matrix is singular as $q \to 1$. For the transformed matrix, the…
We discuss two-parameter deformations of an universal enveloping algebra $U(g[u])$ of a polynomial loop algebra $g[u]$, where $g$ is a finite-dimensional complex simple Lie algebra (or superalgebra). These deformations are Hopf algebras.…
A class of exactly solvable string models can be obtained by starting with flat space and combining T-duality and shifts of angular coordinates of several polar planes. The models are the analog of the Lunin-Maldacena \beta-deformation of…
We use non-Abelian T-duality to construct new N=1 solutions of type IIA supergravity (and their M-theory lifts) that interpolate between AdS_5 geometries. We initiate a study of the holographic interpretation of these backgrounds as RG…
We find new solutions to the Yang-Baxter equations with the $R$-matrices possessing $sl_q(2)$ symmetry at roots of unity, using indecomposable representations. The corresponding quantum one-dimensional chain models, which can be treated as…
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 present a large class of new backgrounds that are solutions of type II supergravity with a warped AdS${}_4$ factor, non-trivial axion-dilaton, B-field, and three- and five-form Ramond-Ramond fluxes. We obtain these solutions by applying…
We construct new families of supersymmetric AdS$_3$ solutions in both massive and massless Type IIA supergravity via deformations to known backgrounds preserving $\mathcal{N} = (4,0)$ and $\mathcal{N} = (6,0)$ supersymmetry. These…
For supercosets with isometry group of the form $\hat{G} \times \hat{G}$, the eta-deformation can be generalised to a two-parameter integrable deformation with independent $q$-deformations of the two copies. We study its kappa-symmetry and…
The impetus for this study is the work of Dumas and Rigal on the Jordanian deformation of the ring of coordinate functions on $2\times 2$ matrices. We are also motivated by current interest in birational equivalence of noncommutative rings.…