course, as in the case of ordinary transition functions, they must satisfy a number of consistency conditions. Exactly what consistency conditions are required has not yet been carefully spelled out. There is a widespread belief that a deeper formulation of the theory ought to exist, and I tend to share that belief, but it is also conceivable that the various perturbation expansions and non-perturbative dualities constitute the best definition of the theory.

Duality Symmetries of Supergravity and Superstring Theories
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There are three types of dualities that appear in superstring theory, which go by the names of $S$, $T$, and $U$. Two theories, call them A and B, are said to be $S$ dual if theory A at strong coupling is equivalent to theory B at weak coupling (and vice versa). This means that there is an exact map between the A and B descriptions that includes, among other things the relation $\phi_A = - \phi_B$. Here $\phi_A$ and $\phi_B$ denote the respective dilaton fields, which determine the string coupling constant $\lambda$ according to the rule $\lambda = {\rm exp} <\phi>$. Theories A and B are called $T$ dual if theory A compactified on a space of large volume is 