Vacua scan of 5d, N=2 consistent truncations

In this letter we present a scan for new vacua within consistent truncations of eleven/ten-dimensional supergravity down to five dimensions that preserve N=2 supersymmetry, after their complete classification in [1]. We first make explicit the link between the equations of exceptional Sasaki-Einstein backgrounds in [2] and the standard BPS equations for 5d N=2 of [3]. This derivation allows us to expedite a scan for vacua preserving N=2 supersymmetry within the framework used for the classification presented in [1].