Reconstruction of Type II Supergravities via $O(d)\times O(d)$ Duality Invariants

We reconstruct type II supergravities by using building blocks of $O(d)\times O(d)$ invariants.These invariants are obtained by explicitly analyzing $O(d)\times O(d)$ transformations of 10 dimensional massless fields. Similar constructions are done by employing double field theory or generalized geometry, but we completed the reconstruction within the framework of the supergravities.