Chiral Liouville Gravity

TL;DR

This paper explores a chiral gauge formulation of two-dimensional Liouville gravity, revealing a residual right Virasoro Kac-Moody symmetry and analyzing its classical structure and potential quantum implications.

Contribution

It introduces a novel chiral gauge for Liouville gravity with residual right Virasoro Kac-Moody symmetry, deriving Dirac brackets and symmetry generators.

Findings

Residual right Virasoro Kac-Moody algebra identified

Dirac brackets of the constrained theory derived

Central charge and Kac-Moody level computed

Abstract

Classical two-dimensional Liouville gravity is often considered in conformal gauge which has a residual left and right Virasoro symmetry algebra. We consider an alternate, chiral, gauge which has a residual right Virasoro Kac-Moody algebra, and no left Virasoro algebra. The Kac-Moody zero mode is the left-moving energy. Dirac brackets of the constrained Hamiltonian theory are derived, and the residual symmetries are shown to be generated by integrals of the conserved chiral currents. The central charge and Kac-Moody level are computed. The possible existence of a corresponding quantum theory is discussed.