Correlation Functions in Two-Dimensional Dilaton Gravity

TL;DR

This paper applies the Liouville approach to quantize two-dimensional dilaton gravity, computes correlation functions, and explores the role of the cosmological term operator in the absence of matter.

Contribution

It provides explicit correlation functions in 2D dilaton gravity using BRST cohomology, highlighting the significance of the cosmological operator's discrete momentum.

Findings

Correlation functions are computed up to three-point functions.

Correlation functions are nonvanishing only for specific chirality configurations.

The cosmological term operator has a discrete momentum playing a key role in the $c=1$ Liouville gravity.

Abstract

The Liouville approach is applied to the quantum treatment of the dilaton gravity in two dimensions. The physical states are obtained from the BRST cohomology and correlation functions are computed up to three-point functions. For the $N=0$ case (i.e., without matter), the cosmological term operator is found to have the discrete momentum that plays a special role in the $c=1$ Liouville gravity. The correlation functions for arbitrary numbers of operators are found in the $N=0$ case, and are nonvanishing only for specific ``chirality'' configurations.