The off-shell c-map

Understand

The off-shell version of the c-map is presented, based on a systematic off-shell reduction from four to three space-time dimensions for supergravity theories with eight supercharges.

• In the reduction, the R-symmetry group is enhanced to local [SU(2) x SU(2)]/Z2 =SO(4) and the c-map is effected by a parity transformation in the internal space that interchanges the two SU(2) factors.
• Vector and tensor supermultiplets are each others conjugate under the c-map and both can be dualized in three dimensions to (on-shell) hypermultiplets.
• As shown in this paper the off-shell formulation indeed leads to a clarification of many of the intricate issues that play a role in the c-map.