Yangian algebra and correlation functions in planar Gauge theories

In this work we consider colour-ordered correlation functions of the fields in integrable planar gauge theories such as \superN=4 supersymmetric Yang–Mills theory with the aim to establish Ward–Takahashi identities corresponding to Yangian symmetries. To this end, we discuss the Yangian algebra relations and discover a novel set of bi-local gauge symmetries for planar gauge theories. We fix the gauge, introduce local and bi-local BRST symmetries and propose Slavnov–Taylor identities corresponding to the various bi-local symmetries. We then verify the validity of these identities for several correlation functions at tree and loop level. Finally, we comment on the possibility of quantum anomalies for Yangian symmetry.

YANGIAN DEFORMATION OF THE LIE ALGEBRA dĩff(T2)

New solution of a classical Yang–Baxter equation on a loop extended, "modified" Lie algebra of a diffeomorphism group of a torus dĩff(T2)[λ]is given. Lie bialgebra structure on dĩff(T2)[λ] is defined. By quantization of a defined Lie bialgebra, a Yangian algebra Y(dĩff(T2)) is obtained. Existence of a quantum double and a quantum R-matrix for Y(dĩff(T2)) is considered.

Multiparametric and Colored Extensions of the Quantum Group GLq(N) and the Yangian Algebra Y(glN) Through a Symmetry Transformation of the Yang–Baxter Equation

Inspired by Reshetikhin's twisting procedure to obtain multiparametric extensions of a Hopf algebra, a general "symmetry transformation" of the "particle conserving" R-matrix is found such that the resulting multiparametric R-matrix, with a spectral parameter as well as a color parameter, is also a solution of the Yang–Baxter equation (YBE). The corresponding transformation of the quantum YBE reveals a new relation between the associated quantized algebra and its multiparametric deformation. As applications of this general relation to some particular cases, multiparametric and colored extensions of the quantum group GL q(N) and the Yangian algebra Y(glN) are investigated and their explicit realizations are also discussed. Possible interesting physical applications of such extended Yangian algebras are indicated.

Algebra of Nonlocal Charges in Supersymmetric Nonlinear Sigma Models

We propose a graphic method to derive the classical algebra (Dirac brackets) of nonlocal conserved charges in the two-dimensional supersymmetric nonlinear O(N) sigma model. As in the purely bosonic theory we find a cubic Yangian algebra. We also consider the extension of graphic methods to other integrable theories.

YANGIAN SYMMETRY OF THE TWO-COMPONENT FERMIONIC NONLINEAR SCHRÖDINGER MODEL

The quantum nonlinear Schrödinger model with two-component fermions exhibits a Yangian symmetry when considered on an infinite interval. We construct the generators of the Yangian using one representation of the degenerate affine Hecke algebra. We discuss the connection between the Yangian symmetry and the quantum inverse scattering method. Under the Yangian algebra the space of states with a fixed particle number forms a tensor product representation of fundamental representations.