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

Abstract

We measure by Monte Carlo simulations ${\text{g}}_{string}$ 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 ${\text{l}}_c$ of the extrinsic curvature coupling and at the transition point the numerically measured value of ${\text{g}}_{string}({\text{l}}_c)\approx 0.27\pm 0.06$. This is consistent with ${\text{g}}_{string}({\text{l}}_c)=1/4$, i.e. equal to the first of the non-trivial values of ${\text{g}}_{string}$ between 0 and $1/2$.

Comments: 11 pages+4 figures, ordinary uncompressed ps-file. NBI-HE-94-39