$SL(\infty ,R)$ Symmetry of $W_{\infty }$ Gravity

Abstract

Two-dimensional gravity in the light-cone gauge was shown by Polyakov to exhibit an underlying $SL(2,R)$ Kac-Moody symmetry, which may be used to express the energy-momentum tensor for the metric component $h_{++}$ in terms of the $SL(2,R)$ currents {\it via}\ the Sugawara construction. We review some recent results which show that in a similar manner, $W_{\infty }$ and $W_{1+\infty }$ gravities have underlying $SL(\infty ,R)$ and $GL(\infty ,R)$ Kac-Moody symmetries respectively.

10 pages (Talk presented at the Trieste Summer School in High-Energy Physics, August 1991)

References in corpus (1)

• Lectures on W algebras and W gravity

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