Two-Dimensional Quantum Gravity on a Disk

TL;DR

This paper investigates two-dimensional quantum gravity on a disk using Liouville theory, calculating boundary correlation functions and revealing complex momentum singularity structures distinct from spherical cases.

Contribution

It provides explicit calculations of boundary correlation functions in 2D quantum gravity on a disk, highlighting differences from sphere topology.

Findings

Computed three-point boundary correlation functions.

Analyzed four-point boundary correlation functions.

Discovered more complex momentum singularity structures.

Abstract

We study a two-dimensional conformal field theory coupled to quantum gravity on a disk. Using the continuum Liouville field approach, we compute three-point correlation functions of boundary operators. The structure of momentum singularities is different from that of correlation functions on a sphere and is more complicated. We also compute four-point functions of boundary operators and three-point functions of two boundary operators and one bulk operator.