Matter fields with c > 1 coupled to 2d gravity

TL;DR

This paper investigates the behavior of matter fields with central charge greater than one coupled to 2D quantum gravity, revealing a transition to branched polymer-like geometries for large central charge and highlighting a universal influence of matter on surface geometry.

Contribution

It provides analytical and numerical evidence that for large central charge, matter coupled to 2D gravity behaves like branched polymers, showing a universal geometric influence.

Findings

No phase transition in branched polymer models with spin systems.

Models with large c resemble branched polymers.

Universal effect of matter on surface geometry depending on total central charge.

Abstract

We solve a class of branched polymer models coupled to spin systems and show that they have no phase transition and are either always magnetized or never magnetized depending on the branching weights. By comparing these results with numerical simulations of two-dimensional quantum gravity coupled to matter fields with central charge $c$ we provide evidence that for $c$ sufficiently large ($c\geq 12$) these models are effectively described by branched polymers. Moreover, the numerical results indicate a remarkable universality in the influence on the geometry of surfaces due to the interaction with matter. For spin systems this influence only depends on the total central charge.