Consistent truncations around half-maximal AdS$_5$ vacua of 11-dimensional supergravity

TL;DR

This paper uses exceptional field theory to classify all consistent truncations around half-maximal AdS5 vacua in M-theory, revealing restrictions on the number of vector multiplets and types of gaugings possible.

Contribution

It systematically characterizes all consistent truncations around these vacua, identifying the limited gaugings and conditions for their existence.

Findings

Only truncations with up to three vector multiplets are consistent.

Possible gaugings are SU(2)×U(1) and ISO(3)×U(1).

ISO(3)×U(1) truncation exists only for specific vacua.

Abstract

We use exceptional field theory to systematically study all possible consistent truncations around half-maximal AdS$_5$ vacua of M-theory. We show that only truncations with at most three vector multiplets are consistent. The possible gaugings are SU(2)$\times$U(1) and ISO(3)$\times$U(1) where, in the first case, the U(1) factor can have different embeddings inside the global symmetry group SO$(5,n)$, where $n \leq 3$ equals the number of vector multiplets. We show that the ISO(3)$\times$U(1) truncation only exists around vacua that are locally an $S^4$ fibration over a Riemann surface, and argue that this is the only consistent truncation with vector multiplets around these vacua that can be constructed by going through the 7-dimensional SO(5) gauged supergravity obtained after an $S^4$ reduction. The consistent truncations with SU(2)$\times$U(1) gaugings with vector multiplets exist only if certain conditions are satisfied, which we derive.