Consistent Two-Dimensional Chiral Gravity

Abstract

We study chiral induced gravity in the light-cone gauge and show that the theory is consistent for a particular choice of chiralities. The corresponding Kac–Moody central charge has no forbidden region of complex values. Generalized analysis of the critical exponents is given and their relation to the SL (2,R) vacuum states is elucidated. All the parameters containing information about the theory can be traced back to the characteristics of the residual symmetry group in the light-cone gauge.