Critical behavior ofn→0 gauge-invariant theory: Self-avoiding random surfaces

We study the critical behavior, in a mean-field approximation, of a grand-canonical ensemble of nonplanar self-avoiding random surfaces (SAS's) which arises as an n{→}0 limit of a gauge-invariant theory. We show explicitly that our model is equivalent to the usual φ⁴ theory near the critical point, with the upper critical dimension equal to 4. The fractal dimension of SAS is 2.