Maximal trombone supergravity from wrapped M5-branes

A new family of maximal supergravities in four dimensions, involving gaugings of the trombone scaling symmetry, has been recently introduced. Using exceptional generalised geometry, we show some supergravities in this class to arise by consistent truncation of $D=11$ supergravity. The seven-dimensional reduction manifold is locally equivalent to the topologically-twisted internal manifold of the AdS$_4$ geometries that arise near the horizon of M5-branes wrapped on supersymmetric three-cycles of special holonomy manifolds. The dimensional reduction involves a mixture of conventional and generalised Scherk-Schwarz prescriptions, and provides the first maximally supersymmetric consistent truncation to four dimensions in the context of the M5-brane.