3D Gravity, Point Particles and Liouville Theory

TL;DR

This paper explores the connection between 3D gravity with negative cosmological constant and Liouville field theory, interpreting certain states as point particles in AdS space and confirming this via semi-classical calculations.

Contribution

It provides a new interpretation of Liouville non-normalizable states as point particles in 3D AdS gravity and confirms this through semi-classical analysis.

Findings

Heavy vertex operators create conical singularities in AdS.

Semi-classical LFT two-point functions match gravity action calculations.

Interpretation links Liouville states to bulk point particles.

Abstract

This paper elaborates on the bulk/boundary relation between negative cosmological constant 3D gravity and Liouville field theory (LFT). We develop an interpretation of LFT non-normalizable states in terms of particles moving in the bulk. This interpretation is suggested by the fact that ``heavy'' vertex operators of LFT create conical singularities and thus should correspond to point particles moving inside AdS. We confirm this expectation by comparing the (semi-classical approximation to the) LFT two-point function with the (appropriately regularized) gravity action evaluated on the corresponding metric.