Twelve-dimensional Effective Action and T-duality

We propose a twelve-dimensional supergravity action, which describes low energy dynamics of F-theory. Dimensional reduction leads the theory to eleven-dimensional, IIA, and IIB supergravities. Self-duality of the four-form field in IIB supergravity is understood. It is necessary to abandon twelve-dimensional Poincare symmetry by making one dimension compact, which is to be decompactified in some region of parameter space, such that the physical degrees of freedom are the same as those of eleven-dimensional supergravity. This makes T-duality explicit as a relation between different compactification schemes.

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