String theory from supergravity and supergravity from string theory

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The rich network of string dualities provides powerful constraints in the structure of the theory. The connection of ten-dimensional type II theories to eleven-dimensional supergravity compactified on a circle and on a torus allows one to compute many perturbative high genus terms as well as the complete sum of non-perturbative contributions to a given higher derivative coupling of the string effective action. The same duality connection leads to a series of surprising non-renormalization theorems. These control the UV behavior of maximal supergravity in lower dimensions, and indicate that N=8 supergravity in four dimensions might be a finite quantum gravity theory.