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

TL;DR

This paper classifies how six-dimensional Einstein-Maxwell supergravity can be embedded into type II supergravity, identifying conditions and solutions, including new classes governed by Toda-like equations, with implications for supersymmetric solutions.

Contribution

It provides a comprehensive classification of embeddings of 6D Einstein-Maxwell supergravity into type II supergravity, including new Toda-like solutions and analysis of various gauging scenarios.

Findings

Two classes of embeddings identified, one governed by a Toda-like equation.

Existence of at least one bounded embedding in the Toda-like class.

Embeddings are more permissive without a tensor multiplet, but PDE complexity increases.

Abstract

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 bounded embedding. In the absence of a tensor multiple the classes of embeddings become more permissive, though the PDEs governing them become more complicated in general.