Abstract
The formal connection between self-avoiding surfaces (SAS) and suitable lattice gauge theories is discussed in the limit that the number of field components goes to zero. Different gauge models correspond to different rules for weighting the SAS topologies or to different constraints imposed on the boundaries. The fractal dimension of a SAS model on a toblerone lattice in d = 2.58… dimensions is calculated exactly. Finally a general qualitative discussion of the behaviour of the SAS in the scaling limit is given in the light of the above and other recent results.
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