A Model of Two-Dimensional Quantum Gravity in the Strong Coupling Regime

TL;DR

This paper proposes a model of two-dimensional quantum gravity analogous to tensionless string theory, revealing that at strong coupling it behaves as a tensionless string in a 2D target space with a quantum mechanical wave function.

Contribution

It introduces a novel model linking 2D quantum gravity to tensionless string theory in the strong coupling regime, with a new interpretation of the wave function.

Findings

At $k ightarrow ty$, 2D quantum gravity resembles tensionless string theory.

The temporal coordinate acts as time in the target space.

Wave function interpretation aligns with standard quantum mechanics.

Abstract

A model of two-dimensional quantum gravity that is the analog of the tensionless string is proposed. The gravitational constant ($k$) is the analog of the Regge slope ($\alpha^{'}$) and it shows that when $k \rightarrow \infty$, $2D$ quantum gravity can be understood as a tensionless string theory embeded in a two-dimensional target space. The temporal coordinate of the target space play the role of time and the wave function can be interpreted as in standard quantum mechanics.