Supersymmetric truncation of N=3 dilaton Weyl multiplet

We perform all possible supersymmetric truncations of the four-dimensional N=3 dilaton Weyl multiplet, which realizes an R-symmetry $SU(2) \times U(1) \times U(1)$, to N=2. A particular truncation procedure does not break any of the R-symmetries and leads to the known N=2 vector-dilaton Weyl multiplet and the N=2 vector multiplet. A different truncation procedure breaks the SU(2) part of the R-symmetry to U(1) and leads to a 32+32 off-shell representation of N=2 conformal supergravity with a partially broken R-symmetry. Independently, we construct another 32+32 off-shell multiplet in N=2 conformal supergravity by coupling the N=2 scalar-tensor multiplet to the N=2 standard Weyl multiplet and using the scalar fields present in the scalar-tensor multiplet to break the SU(2) R-symmetry to U(1). We then establish the equivalence between these two multiplets through a mapping. We observe that this 32+32 multiplet is gauge equivalent to a Poincar\'e supergravity multiplet as it has all the compensators necessary to go from conformal supergravity to Poincar\'e supergravity.