Dimensional reduction of type-II superstrings

As a prototype of a type-II superstring compactified on a (2,2) superconformal field theory, the authors give the explicit expression of the SU(3)-invariant reduction of 10D, type-IIA supergravity to D=4 dimensions. It is shown, as expected from general arguments, that this Lagrangian has a standard N=2 supergravity form as dictated by the N=2 tensor calculus.