Scaling Dimensions of Manifestly Generally Covariant Operators in Two-Dimensional Quantum Gravity

TL;DR

This paper calculates the scaling dimensions of generally covariant operators in 2D quantum gravity coupled to minimal conformal matter using a (2+ε)-dimensional approach, revealing new operators beyond matrix model predictions.

Contribution

It introduces a novel method to compute scaling dimensions in 2D quantum gravity and identifies new operators not accounted for by matrix models.

Findings

Spectrum includes all matrix model scaling dimensions except boundary operators.

Many additional operators are found that do not appear in matrix models.

Partial agreement with matrix models is likely accidental.

Abstract

Using (2+$\epsilon$)-dimensional quantum gravity recently formulated by Kawai, Kitazawa and Ninomiya, we calculate the scaling dimensions of manifestly generally covariant operators in two-dimensional quantum gravity coupled to $(p,q)$ minimal conformal matter. Although the spectrum includes all the scaling dimensions of the scaling operators in the matrix model except the boundary operators, there are also many others which do not appear in the matrix model. We argue that the partial agreement of the scaling dimensions should be considered as accidental and that the operators considered give a new series of operators in two-dimensional quantum gravity.