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

TL;DR

This paper constructs an infinite set of commuting quantum $ abla W_ abla$ charges in the $SL(2,R)/U(1)$ coset model, revealing new integrable structures and quantum flows that preserve the nonlinear current algebra.

Contribution

It explicitly constructs an infinite set of commuting quantum $ abla W_ abla$ charges in the $SL(2,R)/U(1)$ model at $k=1$, demonstrating integrability and compatible quantum flows.

Findings

Infinite commuting quantum $ abla W_ abla$ charges constructed

Quantum flows preserve the $ abla W_ abla$ algebra

Model exhibits integrable quantum structure

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 $\geq 2$ 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.