Consistent two--dimensional chiral gravity

TL;DR

This paper investigates the consistency of two-dimensional chiral gravity in the light-cone gauge, analyzing its algebraic structure and relation to residual symmetries, and clarifies the role of critical exponents and vacuum states.

Contribution

It provides a detailed analysis of the conditions for consistent chiral gravity in two dimensions, including the behavior of the Kac--Moody central charge and the connection to residual symmetries.

Findings

The theory is consistent for specific chiralities.

The Kac--Moody central charge remains real and well-defined.

Critical exponents relate to $SL(2,R)$ vacuum states.

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 group of residual symmetry in the light--cone gauge.