An Infinite Number of Commuting Quantum ${\hat{W}}_{\infty }$ Charges in the $SL(2,R)/U(1)$ Coset Model

Abstract

The conformal non-compact $SL(2,R)/U(1)$ coset model in two dimensions has been recently shown to embody a nonlinear ${\hat{W}}_{\infty }$ current algebra, consisting of currents of spin $\ge 2$ including the energy-momentum tensor. In this letter we explicitly construct an infinite set of commuting quantum ${\hat{W}}_{\infty }$ charges in the model with $k=1$. These commuting quantum charges generate a set of infinitely many compatible flows (quantum KP flows), which maintain the nonlinear ${\hat{W}}_{\infty }$ current algebra invariant.

15p