Scalar potential for the gauged Heisenberg algebra and a non-polynomial antisymmetric tensor theory

We study some issues related to the effective theory of Calabi-Yau compactifications with fluxes in Type II theories. At first the scalar potential for a generic electric abelian gauging of the Heisenberg algebra, underlying all possible gaugings of RR isometries, is presented and shown to exhibit, in some circumstances, a "dual’’ no-scale structure under the interchange of hypermultiplets and vector multiplets. Subsequently a new setting of such theories, when all RR scalars are dualized into antisymmetric tensors, is discussed. This formulation falls in the class of non-polynomial tensor theories considered long ago by Freedman and Townsend and it may be relevant for the introduction of both electric and magnetic charges.