Scale-invariant supergravity theory in component formulation

Abstract

We formulate N=1 supergravity theory in four-dimensions with local scale invariance in semi-on-shell component formulation in four dimensions. The algebra we adopt has the generators (Pm,Mmn,Qα,S) consisting of the generators in super-Poincaré algebra: (Pm,Mmn,Qα) with 4+6+4 components, and that of local scale-transformation S with one additional component. Our field content consists of the on-shell multiplet of supergravity (eμm,ψμα), the tensor multiplet (Bμν,χα,φ) and the ‘Weylon multiplet’ (Sμ,ρα,Cμνρ), where Sμ is the Weylon that gauges local scale symmetry, ψμ,χ and ρ are Majorana spinors, while Cμνρ is a tensor auxiliary field. Similar to the non-supersymmetric case that has no minimal coupling between the Sμ-field and spin 1/2 field, the Weylon does not minimally couple to spin 3/2 gravitino field in our locally supersymmetric generalization. By going to the Einstein frame from the original Jordan frame, we show that our system is equivalent to a system with the gauged dilaton-shift symmetry. This implies that our system bypasses persistent dilaton-related problems, avoiding a long-distance force for a massless dilaton, a minimum value of its potential, or a run-away vacuum.