Discrete Gauge States and$w_\infty$ Charges in c=1 2d Gravity

TL;DR

This paper derives a formula for discrete gauge states in Liouville theory, revealing their $w_ fty$ charges and their role as symmetry parameters, similar to higher-dimensional string theories.

Contribution

It provides a general formula for gauge states at discrete momenta in Liouville theory, highlighting their $w_ abla$ charges and symmetry properties.

Findings

Discrete gauge states carry $w_ abla$ charges.

Gauge states are decoupled from correlation functions.

They serve as symmetry parameters in covariant quantization.

Abstract

We give a general formula for gauge states at the discrete momenta in Liouville theory. These discrete gauge states carry the $w_\infty$ charges. As in the case of the 26D (or 10D) string theory, they are decoupled from the correlation functions and can be considered as the symmetry parameters in the old covariant quantization of the theory.