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

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 $ł_c$ of the extrinsic curvature coupling and at the transition point the numerically measured value of $\g_{string}(ł_c) \approx 0.27\pm 0.06$. This is consistent with $\g_{string}(ł_c)=1/4$, i.e. equal to the first of the non-trivial values of $\g_{string}$ between 0 and $1/2$.