WESS-ZUMINO-WITTEN MODEL-BASED ON A NONSEMISIMPLE GROUP

We present a conformal field theory which describes a homogeneous four dimensional Lorentz-signature space-time. The model is an ungauged We ss-Zumino-Witten model based on a central extension of the Poincare al gebra. The central charge of this theory is exactly four, just like fo ur dimensional Minkowski space. The model can be interpreted as a four dimensional monochromatic plane wave. As there are three commuting is ometries, other interesting geometries are expected to emerge via O(3, 3) duality.