The Two-point Function of c=-2 Matter Coupled to 2D Quantum Gravity

TL;DR

This paper constructs a reparametrization invariant two-point function for c=-2 matter coupled to 2D quantum gravity, deriving critical indices and supporting Fisher's scaling relation using transfer matrix formalism and O(n) model formulation.

Contribution

It introduces a novel method to compute two-point functions in c=-2 matter coupled to quantum gravity, linking string theory and statistical models.

Findings

Derived critical indices  and  for the model.

Confirmed the quantum gravity version of Fisher's scaling relation.

Established a connection between c=-2 string theory and O(n) models on random lattices.

Abstract

We construct a reparametrization invariant two-point function for c=-2 conformal matter coupled to two-dimensional quantum gravity. From the two-point function we extract the critical indices \nu and \eta. The results support the quantum gravity version of Fisher's scaling relation. Our approach is based on the transfer matrix formalism and exploits the formulation of the c=-2 string as an O(n) model on a random lattice.