Is There Quantum Gravity in Two Dimensions?

TL;DR

This paper introduces a hybrid model for two-dimensional quantum gravity that interpolates between different approaches, supporting KPZ exponents and critically examining the absence of gravitational effects in two dimensions.

Contribution

A novel hybrid model bridging Regge approach and dynamical triangulations, enabling fixed geometry analysis and providing numerical evidence for KPZ exponents.

Findings

Supports KPZ exponents in the model

Highlights the lack of gravitational effects in 2D

Provides a critical assessment of 2D quantum gravity

Abstract

A hybrid model which allows to interpolate between the (original) Regge approach and dynamical triangulations is introduced. The gained flexibility in the measure is exploited to study dynamical triangulation in a fixed geometry. Our numerical results support KPZ exponents. A critical assessment concerning the apparent lack of gravitational effects in two dimensions follows.