Related papers: Super Yangian Double and its Central Extension
Drinfeld's degenerate affine analog of Schur-Weyl duality relates representations of the degenerate affine Hecke algebra $AH_r$ to representations of the Yangian $Y_n$. One way to understand the construction is to introduce an intermediate…
The present paper is devoted to extend parabolic presentations, depending on an arbitrary composition of M+N and an arbitrary 01-sequence, of the super Yangian Y(M|N) to a field of positive characteristic.
We give a new proof of the fact that the super Yangian of general linear Lie superalgebra is isomorphic to the finite W-superalgebra of the general linear Lie superalgebra associated to a rectangular nilpotent element.
We give a unified division algebraic description of (D=3, N=1,2,4,8), (D=4, N=1,2,4), (D=6, N=1,2) and (D=10, N=1) super Yang-Mills theories. A given (D=n+2, N) theory is completely specified by selecting a pair (A_n, A_{nN}) of division…
Bars and Sezgin have proposed a super Yang-Mills theory in $D=s+t=11+3$ space-time dimensions with an electric 3-brane that generalizes the 2-brane of M-theory. More recently, the authors found an infinite family of exceptional super…
Using super RS construction method and Gauss decomposition, we obtain Drinfeld's currents realization of two-parameter quantum affine superalgebra $U_{p,q}\widehat{(gl(1|1))}$ and get co-product structure for these currents.
Motivated by the search for a space-time supersymmetric extension of the N=2 string, we construct a particle model which, upon quantization, describes (abelian) self-dual super Yang-Mills in 2+2 dimensions. The local symmetries of the…
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…
The quantum super Yangian $Y_q(gl(M|N))$ associated with the Perk - Schultz solution of the Yang - Baxter equation is introduced. Its structural properties are investigated, in particular, an extensive study of its central algebra is…
We study central extensions of the Lie superalgebra $sl_{m|n}(A)$, where $A$ is a $Z/2Z$-graded superalgebra over a commutative ring $K$. The Steinberg Lie superalgebra $st_{m|n}(A)$ plays a crucial role. We show that $st_{m|n}(A)$ is a…
Division algebras are used to explain the existence and symmetries of various sets of auxiliary fields for super Yang-Mills in dimensions $d=3,4,6,10$. (Contribution to G\"ursey Memorial Conference I: Strings and Symmetries)
In this paper we work out the RTT-realization for the Yangian algebra of the Hubbard model and AdS/CFT correspondence. We find that this Yangian algebra is of a non-standard type in which the levels of the Yangian mix. The crucial feature…
In this paper we review recent results on symmetries in N=4 super Yang-Mills theory. Symmetries are of invaluable help in studying and constraining the scattering amplitudes, and there has been a lot of progress in recent years concerning…
This paper is devoted to the study of the shifted Yangian $Y_n(\sigma)$ associated to the general linear Lie algebra $\mathfrak{gl}_n$ over a field of positive characteristic. We obtain an explicit description of the center $Z(Y_n(\sigma))$…
We present a connection between W-algebras and Yangians, in the case of gl(N) algebras, as well as for twisted Yangians and/or super-Yangians. This connection allows to construct an R-matrix for the W-algebras, and to classify their…
We construct W-algebra generalizations of the ^sl(2) algebra -- W-algebras W^{(2)}_n generated by two currents E and F with the highest pole of order n in their OPE. The n=3 term in this series is the Bershadsky--Polyakov algebra. We define…
We construct a homomorphism from the affine Yangian $Y_{\hbar,\varepsilon+\hbar}(\widehat{\mathfrak{sl}}(n))$ to the affine Yangian $Y_{\hbar,\varepsilon}(\widehat{\mathfrak{sl}}(n+1))$ which is different from the one in arXiv:2312.09933.…
Dialgebras are generalizations of associative algebras which give rise to Leibniz algebras instead of Lie algebras. In this paper we study super dialgebras and Leibniz superalgebras, which are $\z_2$-graded dialgebras and Leibniz algebras.…
We present an action for noncommutative supersymmetric Yang-Mills theory in ten-dimensions, and confirm its invariance under supersymmetry. We next add higher-order derivative terms to such a noncommutative supersymmetric action. These…
We propose an extension of the su(2,2|4) superalgebra to incorporate the $F1/D1$ string charges in type IIB string theory on the $AdS_{5} \times S^{5}$ background, or the electro-magnetic charges in the dual super Yang-Mills theory. With…