Geometrical Properties of Conformal Field Theories Coupled to Two-Dimensional Quantum Gravity

TL;DR

This paper explores the geometric properties of conformal field theories coupled to 2D quantum gravity, using a quasiclassical approach to derive gravitational dressing and the intrinsic Hausdorff dimension of world sheets.

Contribution

It applies F. David's method to reproduce gravitational dressing and compute the Hausdorff dimension in non-critical string theory.

Findings

Reproduces standard gravitational dressing in perturbation theory

Calculates the intrinsic Hausdorff dimension of world sheets

Links conformal dimensions to geometric scaling behaviors

Abstract

In this work we discuss an approach due to F. David to the geometry of world sheets of non-critical strings in quasiclassical approximation. The gravitational dressed conformal dimension is related to the scaling behavior of the two-point function with respect to a distance variable. We show how this approach reproduces the standard gravitational dressing in the next order of perturbation theory. With the same technique we calculate the intrinsic Hausdorff dimension of a world sheet.