Type II embeddings for d = 6 Einstein-Maxwell gauged supergravity

Abstract

A bstract Bi-spinor and G-structure methods are used to classify the possible consistent truncations of type II supergravity to d = 6 Einstein-Maxwell (gauged) supergravity, and its consistent sub-sectors. In the absence of R-symmetry gauging and a tensor multiplet we establish that every supersymmetric Mink 6 solution defines an embedding of the d = 6 theory. Adding a tensor multiplet places restrictions on these embeddings, but embeddings still exist. In the presence of R-symmetry gauging the internal spaces of the embeddings are neither related to Mink 6 or AdS 6 . Under the assumption that the internal space contains a single U(1) isometry housing the d = 6 gauge field we classify the possible embedding manifolds. We find two classes of embedding for the entire theory, one of which is governed by a Toda-like equation and contains at least one prototype bounded embedding, albeit containing likely un-physical singularities. In the absence of a tensor multiple the classes of embeddings become more permissive, though the PDEs governing them become more complicated in general.