Related papers: A Yangian Double for the AdS/CFT Classical r-matri…
It is argued that the integrable model for the planar spectrum of the AdS/CFT correspondence can accommodate for the full spectrum of excitations $D^{\alpha \dot \alpha}, \phi^{[IJ]}, \psi^I, \bar \psi_I, F^{\alpha \beta}, \tilde F^{\dot…
We start from known solutions of the Yang-Baxter equation with a spectral parameter defined on the tensor product of two infinite-dimensional principal series representations of the group $\mathrm{SL}(2,\mathbb{C})$ or Faddeev's modular…
Starting with any R-matrix with spectral parameter, obeying the Yang-Baxter equation and a unitarity condition, we construct the corresponding infinite dimensional quantum group U_{R} in term of a deformed oscillators algebra A_R. The…
Quantum doubles of finite group algebras form a class of quasi-triangular Hopf algebras which algebraically solve the Yang--Baxter equation. Each representation of the quantum double then gives a matrix solution of the Yang--Baxter…
For every family of orthogonal polynomials, we define a new realization of the Yangian of ${\mathfrak{gl}}_n$. Except in the case of Dickson polynomials, the new realizations do not satisfy the RTT relation. We obtain an analogue of the…
We study a certain family of finite-dimensional simple representations over quantum affine superalgebras associated to general linear Lie superalgebras, the so-called fundamental representations: the denominators of rational $R$-matrices…
Scaling limits when q tends to 1 of the elliptic vertex algebras A_qp(sl(N)) are defined for any N, extending the previously known case of N=2. They realise deformed, centrally extended double Yangian structures DY_r(sl(N)). As in the…
Various classes of fishnet Feynman graphs are shown to feature a Yangian symmetry over the conformal algebra. We explicitly discuss scalar graphs in three, four and six spacetime dimensions as well as the inclusion of fermions in four…
We consider the exact $R$-matrix of $AdS_3/CFT_2$, which is the building block for describing the scattering of worldsheet excitations of the light-cone gauge-fixed backgrounds $AdS_3 \times S^3 \times T^4$ and $AdS_3 \times S^3 \times S^3…
An interesting type of spin chain has appeared in the context of the planar AdS/CFT correspondence: It is based on an integrable nearest-neighbor spin chain, and it is perturbatively deformed by long-range interactions which apparently…
We connect generalizations of Poisson algebras with the classical and associative Yang-Baxter equations. In particular, we prove that solutions of the classical Yang-Baxter equation on a vector space V are equivalent to ``twisted'' Poisson…
Non linear sigma models on Riemannian symmetric spaces constitute the most general class of classical non-linear sigma models which are known to be integrable. Using the current algebra structure of these models their canonical structure is…
We discuss applications of the $q$-characters to the computation of the $R$-matrices. In particular, we describe the $R$-matrix acting in the tensor square of the first fundamental representation of E$_8$ and in a number of other cases,…
We propose and study a holographic dual of the type IIB superstring theory of AdS_5 x S^5 in terms of the N=4 superconformal Yang-Mills theory on dS_4. We use the bulk to boundary formalism to evaluate the boundary correlation functions and…
The recent developments towards the possible non-perturbative formulation of string/M theory using supersymmetric Yang-Mills matrix models (SYMs) are discussed. In the first part, we give a critical review on the status of our present…
We propose that chiral two-dimensional Yang-Mills theory on a Riemann surface is dual to a deformed stationary subsector of the Gromov-Witten theory of that Riemann surface. Firstly, we argue that the algebraic structure that underlies the…
AdS/CFT-correspondence establishes a relationship between supersymmetric gravity (SUGRA) on Anti-de-Sitter (AdS) space and supersymmetric Yang-Mills (SYM) theory which is conformaly invariant (CFT). The AdS space is the solution of the…
We build string backgrounds for Yang-Baxter deformations of the $AdS_4\times\mathbb{CP}^3$ superstring generated by $r$-matrices satisfying the classical Yang-Baxter equation. We obtain the metric and the NS-NS two-form of the gravity dual…
We review recent progress on computing scattering amplitudes of planar N=4 super Yang-Mills at strong coupling by using the AdS/CFT duality. We do explicit computations by using both, dimensional regularization and a cut-off in the radial…
Studies of noncommutative gauge theory have mainly focused on noncommutative spacetimes with constant noncommutative structure, with little known about actions for noncommutative 4D Yang-Mills theory beyond this case. We construct an action…