N =4 Supergravity with Local Scaling Symmetry in Four Dimensions

A bstract We construct the most general four-dimensional N N = 4 supergravity coupled to an arbitrary number n of vector multiplets in which the global scaling symmetry is gauged, in addition to a subgroup of SL (2, ℝ) × SO (6, n). The various gaugings are parametrized by an embedding tensor built out of 2 (arraycn+6\\ 3array) +4 (n+6) 2 n + 6 3 + 4 n + 6 parameters that satisfy a specific set of quadratic consistency constraints, to which we provide explicit solutions. We also derive the local supersymmetry transformation rules and the equations of motion for the four-dimensional N N = 4 matter-coupled supergravity with local scaling symmetry. Such supergravity theories do not possess an action, since the scaling symmetry is only an on-shell symmetry of the corresponding ungauged theories.