c = 1 Two Dimensional Quantum Gravity

TL;DR

This paper reviews the continuum approach to 2D quantum gravity with c=1 matter, discusses physical states and correlation functions, and reports new results on dilaton gravity using BRST cohomology.

Contribution

It provides a detailed analysis of physical states and correlation functions in 2D quantum gravity at c=1, including new insights into dilaton gravity and string field theory.

Findings

Physical states identified via BRST cohomology.

Correlation functions computed for 2D quantum gravity.

New results on dilaton gravity related to c=1 matter.

Abstract

The continuum (Liouville) approach to the two-dimensional (2-D) quantum gravity is reviewed with particular attention to the $c=1$ conformal matter coupling, and new results on a related problem of dilaton gravity are reported. After finding the physical states, we examine the procedure to compute correlation functions. The physical states in the relative cohomology show up as intermediate state poles of the correlation functions. The states in the absolute cohomology but not in the relative cohomology arise as auxiliary fields in string field theory. The Liouville approach is applied also to the quantum treatment of the dilaton gravity. The physical states are obtained from the BRST cohomology and correlation functions are computed in the dilaton gravity.