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We use exceptional field theory to systematically study all possible consistent truncations around any  M -theory half-maximal vacua of the warped product form AdS 5  ×  M 3  ×  S 2  ×  S 1 , with  M 3  a three-dimensional manifold. We show that, for any of these vacua, only truncations with at most three vector multiplets are consistent. Furthermore, the possible gaugings are restricted to be either SU(2) × U(1) or ISO(3) × U(1) where, in the first case, the U(1) factor can have different embeddings inside the global symmetry group SO(5,  n ), where  n  ⩽ 3 equals the number of vector multiplets. This rules out the possibility of any other gauging arising as a consistent truncation around the aforementioned  M -theory vacua. Our analysis shows that of the many flows from half-maximal to quarter-maximal AdS 5  vacua constructed in five-dimensional supergravity in Bobev (2018  J. High Energy Phys.  6  86), only those corresponding to an adjoint mass deformation in the dual SCFT can be uplifted to 11-dimensional supergravity. The other flows are five-dimensional artefacts without a higher-dimensional origin. Furthermore, consistent truncations with vector multiplets exist only if the vacuum satisfies certain conditions, which we derive.

Consistent truncations around half-maximal AdS5 vacua of 11-dimensional supergravity

Consistent truncations around half-maximal AdS₅ vacua of 11-dimensional supergravity