A note on 2D chiral gravity and chiral bosons

Quantization of two dimensional chiral matter coupled to gravity induces an effective action for the zweibein field which is both Weyl and Lorentz anomalous. Recently, the quantization of this induced action has been analyzed in the light-cone gauge as well as in the conformal gauge. An apparent mismatch between the results obtained in the two gauges is analyzed and resolved by properly treating the Lorentz field as a chiral boson.