Related papers: Instanton R-matrix and W-symmetry
We study the Yangians Y(a) associated with the simple Lie algebras a of type B, C or D. The algebra Y(a) can be regarded as a quotient of the extended Yangian X(a) whose defining relations are written in an R-matrix form. In this paper we…
Following Braverman-Finkelberg-Feigin-Rybnikov (arXiv:1008.3655), we study the convolution algebra of a handsaw quiver variety, a.k.a. a parabolic Laumon space, and a finite W-algebra of type A. This is a finite analog of the AGT conjecture…
We study deformations of the quantum conformal mechanics of De Alfaro-Fubini-Furlan with rational additional potential term generated by applying the generalized Darboux-Crum-Krein-Adler transformations to the quantum harmonic oscillator…
The emergence of the quantum $R$-matrix in the double-scaled SYK model points to an underlying quantum group structure. In this work, we identify the quantum group $\mathcal{U}_q(\mathfrak{su}(1,1))$ as a subalgebra of the chord algebra.…
We find the exact matrix model description of two dimensional Yang-Mills theories on a cylinder or on a torus and with an arbitrary compact gauge group. This matrix model is the singlet sector of a $c =1$ matrix model where the matrix field…
Yang-Baxter relations symmetric with respect to the ortho-symplectic superalgebras are studied. We start from the formulation of graded algebras and the linear superspace carrying the vector (fundamental) representation of the…
We describe the construction of trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two irreducible representations of a quantum algebra $U_q(\G)$. Our method is a generalization of the tensor product…
The problem about geometric correspondence of Dirac particle and contain quality item of Yang-Mills equation has always not been solved.This paper introduced the hyperbolic imaginary unit in Minkowski space, established a classes of Dirac…
We present an integral representation to the quantum Knizhnik-Zamolodchikov equation associated with twisted affine symmetry $U_q(A_2^{(2)})$ for massless regime $|q|=1$. Upon specialization, it leads to a conjectural formula for the…
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…
Using the covariant phase space formalism, we construct the phase space for non-Abelian gauge theories in $(d+2)$-dimensional Minkowski spacetime for any $d \geq 2$, including the edge modes that symplectically pair to the low energy…
In this paper we derive the universal R-matrix for the Yangian Y(u(2|2)), which is an abstract algebraic object leading to rational solutions of the Yang-Baxter equation on representations. We find that on the fundamental representation 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…
We classify the finite-dimensional irreducible representations of the super Yangian associated with the orthosymplectic Lie superalgebra ${\frak osp}_{2|2n}$. The classification is given in terms of the highest weights and Drinfeld…
We study the instanton effective action of four-dimensional deformed N=4 supersymmetric Yang-Mills theory in the presence of constant, self-dual Ramond-Ramond (R-R) 3-form background in type IIB superstring theory. We compare the instanton…
In our preceding research, we introduced the Drinfeld presentation of the quantum affine superalgebra associated to the orthosymplectic Lie superalgebra $\mathfrak{osp}(2m+1|2n)$ for $m>0$. We provided the isomorphism between its…
We show that for F an invertible 2 by 2 matrix, the von Neumann algebra associated to the universal quantum group A_u(F) is a free Araki-Woods factor.
A new approach to the construction of interacting quantum field theories on two-dimensional Minkowski space is discussed. In this program, models are obtained from a prescribed factorizing S-matrix in two steps. At first, quantum fields…
We study the truncated shifted Yangian $Y_{n,l}(\sigma)$ over an algebraically closed field $\mathbb{k}$ of characteristic $p > 0$, which is known to be isomorphic to the finite $W$-algebra $U(\mathfrak{g}, e)$ associated to a corresponding…
We study the quantum effects on the Coulomb branch of N=2 SU(2) supersymmetric Yang-Mills with fundamental matters compactified on R^3 x S^1, and extract the explicit perturbative and leading non-perturbative corrections to the moduli space…