A Random Surface Theory with Non-Trivial $\gamma_{string}$

TL;DR

This paper uses Monte Carlo simulations to study a model of random surfaces with extrinsic curvature, finding a phase transition where the string susceptibility exponent takes a non-trivial value around 0.27, close to 1/4.

Contribution

It provides numerical evidence for a non-trivial string susceptibility exponent at a phase transition in a random surface model with extrinsic curvature.

Findings

Identifies a phase transition at finite extrinsic curvature coupling.

Measures the string susceptibility exponent near 0.27 at the transition.

Finds consistency with the theoretical value of 1/4 for the exponent.

Abstract

We measure by Monte Carlo simulations $\g_{string}$ for a model of random surfaces embedded in three dimensional Euclidean space-time. The action of the string is the usual Polyakov action plus an extrinsic curvature term. The system undergoes a phase transition at a finite value $\l_c$ of the extrinsic curvature coupling and at the transition point the numerically measured value of $\g_{string}(\l_c) \approx 0.27\pm 0.06$. This is consistent with $\g_{string}(\l_c)=1/4$, i.e. equal to the first of the non-trivial values of $\g_{string}$ between 0 and $1/2$.