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

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

1992-01-13

arxiv.org/abs/hep-th/9201023v1

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1016/0550-3213(92)90067-L

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.

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