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arXiv · hep-th/9112009

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

Feng Yu·Yong-Shi Wu
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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 $k=9/4$.

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Feng Yu, Yong-Shi Wu. 1991-12-04. Nonlinear $\hat{W}_{\infty}$ Current Algebra in the SL(2,R)/U(1) Coset Model. https://doi.org/10.1103/physrevlett.68.2996

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