Four Dimensional 2-Brane Solution in Chiral Gauged Wess-Zumino-Witten Model

An exact conformal field theory describing a four dimensional 2-brane solution is found by considering a chiral gauged Wess-Zumino -Witten theory corresponding to $SL(2, R)\times R$ , where one gauges the one dimensional $U(1)$ subgroup together with a translation in $R$. The backgrounds for string propagation are explicitly obtained and the target space is shown to have a true curvature singularity.