Nonlinear ${\hat{W}}_{\infty }$ Current Algebra in the SL(2,R)/U(1) Coset Model

Abstract

Previously we have established that the second Hamiltonian structure of the KP hierarchy is a nonlinear deformation, called ${\hat{W}}_{\infty }$, of the linear, centerless $W_{\infty }$ algebra. In this letter we present a free-field realization for all generators of ${\hat{W}}_{\infty }$ in terms of two scalars as well as an elegant generating function for the ${\hat{W}}_{\infty }$ currents in the classical conformal $SL(2,R)/U(1)$ coset model. After quantization, a quantum deformation of ${\hat{W}}_{\infty }$ appears as the hidden current algebra in this model. The ${\hat{W}}_{\infty }$ current algebra results in an infinite set of commuting conserved charges, which might give rise to $W$-hair for the 2d black hole arising in the corresponding string theory at level $k=9/4$.

11p

References in corpus (1)

• On the connection between Quantum Mechanics and the geometry of two-dimensional strings

Cited by in corpus (24)

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