On the fakeness of fake supergravity

We revisit and complete the study of curved BPS-domain walls in matter-coupled 5D, N=2 supergravity and carefully analyse the relation to gravitational theories known as "fake supergravities". We first show that \emph{curved} BPS-domain walls require the presence of non-trivial hypermultiplet scalars, whereas walls that are solely supported by vector multiplet scalars are necessarily \emph{flat}, due to the constraints from very special geometry. We then recover fake supergravity as the effective description of true supergravity where one restricts the attention to the flowing scalar field of a given BPS-domain wall. In general, however, true supergravity can be simulated by fake supergravity at most \emph{locally}, based upon two choices: (i) a suitable adapted coordinate system on the scalar manifold, such that only one scalar field plays a dynamical role, and (ii) a gauge fixing of the SU(2) connection on the quaternionic-Kahler manifold, as this connection does not fit the simple formalism of fake supergravity. Employing these gauge and coordinate choices, the BPS-equations for both vector and hypermultiplet scalars become identical to the fake supergravity equations, once the line of flow is determined by the full supergravity equations.