A note on 2D chiral gravity and chiral bosons

TL;DR

This paper examines the quantization of 2D chiral gravity coupled with chiral bosons, addressing gauge-related discrepancies and clarifying the role of Lorentz anomalies in the effective action.

Contribution

It provides a detailed analysis of gauge-dependent results in 2D chiral gravity and resolves apparent mismatches by properly treating the Lorentz field as a chiral boson.

Findings

Resolved gauge discrepancies in the quantization process.

Clarified the role of Lorentz anomalies in the effective action.

Highlighted the importance of proper Lorentz field treatment.

Abstract

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.