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We show how to construct supersymmetric warped AdS$_7$ vacua of massive IIAand AdS$_6$ vacua of IIB supergravity, using "half-maximal structures" ofexceptional field theory. We use this formalism to obtain the minimalconsistent truncations around these AdS vacua.

Supersymmetric AdS$_{7}$ and AdS$_6$ vacua and their minimal consistent truncations from exceptional field theory