$SL(\infty,R)$ Symmetry of $W_\infty$ Gravity
arXiv:hep-th/9201023 · doi:10.1016/0550-3213(92)90067-L
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)