PSU(2,2|4) Exchange Algebra of N=4 Superconformal Multiplets

Abstract

It is known that the unitary representation of the D=4, N=4 superconformal multiplets and their descendants are constructed as supercoherent states of bosonic and fermionic creation oscillators which covariantly transform under SU(2,2|4). We non-linearly realize those creation oscillators on the coset superspace PSU(2,2|4)/{SO(1,4) x SO(5)} which is reparametrized by the D=10 supercoordinates. We consider a D=2 non-linear sigma model on the coset superspace and set up Poisson brackets for the D=10 supercoordinates on the light-like line. It is then shown that the non-linearly realized creation oscillators satisfy the classical exchange algebra with the classical r-matrix of PSU(2,2|4). We have recourse to purely algebraic quantization of the classical exchange algebra in which the r-matrix is promoted to the universal R-matrix. The quantum exchange algebra essentially characterizes correlation functions of the D=4, N=4 superconformal multiplets and their descendants on the light-like line. The arguments are straightforwardly extended to the case where those quantities are endowed with the U(N) YM gauge symmetry.