A 24+24 real scalar multiplet in four dimensional N=2 conformal supergravity

Starting from the 48+48 component multiplet of supercurrents for a rigid N=2 tensor multiplet in four spacetime dimensions, we obtain the transformation of the linearized supergravity multiplet which couples to this supercurrent multiplet. At the linearized level, this 48+48 component supergravity multiplet decouples into the 24+24 component linearized standard Weyl multiplet and a 24+24 component irreducible matter multiplet containing a real scalar field. By a consistent application of the supersymmetry algebra with field dependent structure constants appropriate to N=2 conformal supergravity, we find the full transformation law for this multiplet in a conformal supergravity background. By performing a field redefinition and switching off the conformal supergravity background, the multiplet is equivalent to the one introduced by Howe et al in flat space as a constrained real scalar superfield. We present a set of constraints which can be consistently imposed on this multiplet to obtain a restricted minimal 8+8 off-shell matter multiplet. We also show as an example the precise embedding of the tensor multiplet inside this multiplet.