Twelve-dimensional effective action and T-duality

We propose a 12-dimensional supergravity action which describes low-energy dynamics of $$F$$F-theory. Dimensional reduction leads the theory to become 11-dimensional, IIA, and IIB supergravities. Self-duality of the four-form field in IIB supergravity is understood. It is necessary to abandon 12-dimensional Poincaré 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 11-dimensional supergravity. This makes $$T$$T-duality explicit as a relation between different compactification schemes.