Properties of the wormhole-dominant phase in two-dimensional quantum gravity

TL;DR

This paper investigates how wormhole effects influence two-dimensional quantum gravity by analyzing a modified matrix model, revealing that wormholes can significantly alter the critical behavior and effective cosmological constant.

Contribution

It introduces a renormalized coupling for the double-trace interaction, showing its impact on the bulk cosmological constant in 2D quantum gravity.

Findings

Wormhole effects can change the critical behavior of 2D quantum gravity.

The continuum disk amplitude remains unchanged by wormholes at the critical point.

Renormalized coupling effectively modifies the bulk cosmological constant.

Abstract

We study the $N \times N$ Hermitian one-matrix model modified by the double-trace interaction. It is known that the coupling for the double-trace interaction can control the weight for the microscopic wormholes if interpreting the matrix model as the lattice model of random surface; tuning the coupling to its critical value, the effect of wormholes become substantial to change the critical behavior of the pure $2$D quantum gravity, which is characterized by a certain positive value of the string susceptibility. In the large-$N$ limit, we calculate the continuum limit of the disk amplitude in which the wormhole effects are important. The resulting continuum disk amplitude is the same as that of the pure $2$D quantum gravity. We also introduce the renormalized coupling for the double-trace interaction, and show that the newly introduced renormalized coupling can alter the renormalized bulk cosmological constant effectively.