The R-map and the coupling of Script N = 2 tensor multiplets in 5 and 4 dimensions

We study the dimensional reduction of 5D, = 2 Yang-Mills-Einstein supergravity theories (YMESGT) coupled to tensor multiplets. The resulting 4D theories involve first order interactions among tensor and vector fields with mass terms. If the 5D gauge group, K, does not mix the 5D tensor and vector fields, the 4D tensor fields can be integrated out in favor of the 4D vector fields and the resulting theory is dual to a standard 4D YMESGT (Integrating out the vector fields in favor of tensor fields instead seems to require nonlocal field redefinitions). The gauge group has a block diagonal symplectic embedding and is a semi-direct product of the 5D gauge group K with a Heisenberg group nT+1 of dimension nT+1, where nT is the number of tensor fields in five dimensions. There exists an infinite family of theories, thus obtained, whose gauge groups are pp-wave contractions of the simple noncompact groups of type SO*(2N). If, on the other hand, the 5D gauge group does mix the 5D tensor and vector fields, the resulting 4D theory is dual to a 4D YMESGT whose gauge group does, in general, not have a block diagonal symplectic embedding and involves additional topological terms. The scalar potentials of the dimensionally reduced theories studied in this paper naturally have some of the ingredients that were found necessary for stable de Sitter ground states in earlier studies. We comment on the relation between the known 5D and 4D, = 2 supergravities with stable de Sitter ground states.