Related papers: On Drinfeld's second realization of the AdS/CFT su…
We explore the idea to bootstrap Feynman integrals using integrability. In particular, we put the recently discovered Yangian symmetry of conformal Feynman integrals to work. As a prototypical example we demonstrate that the D-dimensional…
We consider supersymmetric AdS$_3 \times Y_7$ and AdS$_2 \times Y_9$ solutions of type IIB and $D=11$ supergravity, respectively, that are holographically dual to SCFTs with $(0,2)$ supersymmetry in two dimensions and $\mathcal{N}=2$…
Applying the method of the paper [CT], we perform a quantum version of the Drinfeld-Sokolov reduction in Reflection Equation algebras and braided Yangians, associated with involutive and Hecke symmetries of general forms. This reduction is…
We provide a direct proof of the Drinfeld realization for the quantum affine algebras.
We uncover a general principle, dubbed c-extremization, which determines the exact R-symmetry of a two-dimensional unitary superconformal field theory with N=(0,2) supersymmetry. To illustrate its utility, we study superconformal theories…
We give a new presentation of the Drinfeld double of the elliptic Hall algebra introduced in a previous work with I. Burban. This presentation is similar in spirit to Drinfeld's `new realization' of quantum affine algebras. This answers, in…
We study the double Yangian associated with the Lie superalgebra $\mathfrak{gl}_{m|n}$. Our main focus is on establishing the Poincar\'{e}-Birkhoff-Witt Theorem for the double Yangian and constructing its central elements in the form of…
This review is meant to be an account of the properties of the infinite-dimensional quantum group (specifically, Yangian) symmetry lying behind the integrability of the AdS/CFT spectral problem. In passing, the chance is taken to give a…
Based on the formulation of Drinfel'd, Chari, and Pressley, a technique to analyze the structure of tensor products of the Yangian algebra representations is presented. We then apply the results to the $S$-matrix theory of the $G\otimes…
We give the principal realization of the twisted Yangians of orthogonal and symplectic types. The new bases are interpreted in terms of discrete Fourier transform over the cyclic group Z_N.
Analogs of the classical Sylvester theorem have been known for matrices with entries in noncommutative algebras including the quantized algebra of functions on GL(N) and the Yangian for gl(N). We prove a version of this theorem for the…
In \cite{S} O. Schiffmann gave a presentation of the Drinfel'd double of the elliptic Hall algebra which is similar in spirit to Drinfel'd's new realization of quantum affine algebras. Using this result together with a part of his proof we…
We introduce some techniques for making a more global analysis of the existence of geodesics on a Seiberg-Witten Riemann surface with metric $ds^2 = |\lambda_{SW}|^2$. Because the existence of such geodesics implies the existence of BPS…
We give the overview of solution techniques for the general conformally-invariant linear and nonlinear wave equations centered around the idea of dimensional reductions by their symmetry groups. The efficiency of these techniques is…
The affine Yangian of $\mathfrak{gl}_1$ is known to be isomorphic to ${\cal W}_{1+\infty}$, the $W$-algebra that characterizes the bosonic higher spin -- CFT duality. In this paper we propose defining relations of the Yangian that are…
A weight basis for each finite-dimensional irreducible representation of the orthogonal Lie algebra o(2n) is constructed. The basis vectors are parametrized by the D-type Gelfand--Tsetlin patterns. Explicit formulas for the matrix elements…
Drinfeld zastava is a certain closure of the moduli space of maps from the projective line to the Kashiwara flag scheme of an affine Lie algebra $\hat g$. In case $g$ is the symplectic Lie algebra $sp_N$, we introduce an affine, reduced,…
We investigate the Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory and show that its formulations in twistor and momentum twistor space can be interchanged. In particular we show that the full symmetry can be…
We use the Dunkl operator approach to construct one dimensional integrable models describing N particles with internal degrees of freedom. These models are described by a general Hamiltonian belonging to the center of the Yangian or the…
The two-parameter quantum vertex operator representation of level-one is explicitly constructed for $U_{r,s}(C^{(1)}_n)$ based on its two-parameter Drinfeld realization we give. This construction will degenerate to the one-parameter case…