In this section, we describe some large scale parallel simulations of dynamically triangulated random surfaces [Baillie:90c], [Baillie:90d], [Baillie:90e], [Baillie:90j], [Baillie:91c], [Bowick:93a]. Dynamically triangulated random surfaces have been suggested as a possible discretization for string theory in high energy physics and fluid surfaces or membranes in biology [Lipowski:91a]. As physicists, we shall focus on the former.

String theories describe the interaction of one-dimensional string-like objects in a fashion analogous to the way particle theories describe the interaction of zero-dimensional point-like particles. String theory has its genesis in the dual models that were put forward in the 1960s to describe the behavior of the hadronic spectrum then being observed. The dual model amplitudes could be derived from the quantum theory of a stringlike object [Nambu:70a], [Nielsen:70a], [Susskind:70a]. It was later discovered that these so-called bosonic strings could apparently only live in 26 dimensions [Lovelace:68a] if they were to be consistent quantum-mechanically. They also had tachyonic (negative mass-squared) ground states, which is normally the sign of an instability. Later, fermionic degrees of freedom were added to the theory, yielding the supersymmetric Neveu-Schwarz-Ramond [Neveu:71a] (NSR) string. This has a critical dimension of 10, rather than 26, but still suffers from the tachyonic ground state. Around 1973, it became clear that QCD provided a plausible candidate for a model of the hadronic spectrum, and the interest in string models of hadronic interactions waned. However, about this time it was also postulated by numerous groups that strings [Scherk:74a] might provide a model for gravity because of the prescence of higher spin excitations in a natural manner. A further piece of the puzzle fell into place in 1977 when [Gliozzi:77a] found a way to remove the tachyon from the NSR string. The present explosion of work on string theory began with the work of Green and Schwarz [Green:84a], who found that only a small number of string theories could be made tachyon free in 10 dimensions, and predicted the occurrence of one such that had not yet been constructed. This appeared soon after in the form of the heterotic string [Gross:85a], which is a sort of composite of the bosonic and supersymmetric models.

After these discoveries, the physics community leaped on string models as a way of constructing a unified theory of gravity [Schwarz:85a]. Means were found to compactify the unwanted extra dimensions and produce four-dimensional theories that were plausible grand unified models, that is, models which include both the standard model and gravity. Unfortunately, it now seems that much of the predictive power that came from the constraints on the 10-dimensional theories is lost in the compactification, so interest in string models for constructing grand unified theories has begun to fade. However, considered as purely mathematical entities, they have led and are leading to great advances in complex geometry and conformal field theory. Many of the techniques that have been used in string theory can also be directly translated to the field of real surfaces and membranes, and it is from this viewpoint that we want to discuss the subject.

Wed Mar 1 10:19:35 EST 1995