Recursive sampling simulations of 3D gravity coupled to scalar fermions

TL;DR

This paper investigates the phase structure of 3D gravity coupled with scalar fermions using numerical simulations, revealing two phases separated by a critical point and drawing parallels with 2D simplicial gravity.

Contribution

It provides the first numerical analysis of 3D gravity with scalar fermions, identifying phase transitions and relating the inverse Newton coupling to matter central charge.

Findings

Two phases separated by a critical point at α ≈ 2

The 3D string susceptibility exponent varies with α

Qualitative similarity between 3D and 2D gravity phase structures

Abstract

We study numerically the phase structure of a model of 3D gravity interacting with scalar fermions. We measure the 3D counterpart of the "string" susceptibility exponent as a function of the inverse Newton coupling $\alpha$. We show that there are two phases separated by a critical point around $\alpha_c \simeq 2$. The numerical results support the hypothesis that the phase structures of 3D and 2D simplicial gravity are qualitatively similar, the inverse Newton coupling in 3D playing the role of the central charge of matter in 2D.