Abstract
We present simple models which exhibit some of the remarkable featuresexpected to hold for the as yet unknown non-perturbativeformulation of string theories.Among these are: (a) the absence of a background or embedding space forthefull theory; (b) perturbative ground states (local minima of the action)having the characteristics of spaces of differentdimension; (c) duality transformations between large- and small-couplingexpansions; and (d) perturbative excitations ofthese ground states which can be interpreted asstring worldsheets or p-brane worldvolumes.In this context we formulate gauge theories on arbitrary graphs andspeculate concerning actions for graphs which in a continuum and/orthermodynamiclimit might be related to the Einstein-Hilbert action.
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