Interplay of Intersecting Branes and Consistent Embeddings

TL;DR

Interplay of intersecting branes and consistent embeddings develops a two-way framework linking higher-dimensional brane intersections to worldvolume consistent truncations (skeleton-brane embeddings). It introduces a new family of fully localised-component intersecting-brane solutions that inform, and are informed by, embedding ansätze for pure supergravity on brane worldvolumes, with explicit bosonic embeddings for 5d $N=4$ on D4 and 6d $N=(1,1)$ on NS5 in type II theory. The work demonstrates concrete D3- and M5-brane examples that realize $N=4$ in 4d and $N=(2,0)$ in 6d on the skeleton, respectively, and provides systematic methods to infer and prove consistency of the embeddings (with fermionic sectors treated in appendices). The results offer a path toward holographic descriptions in near-horizon limits and motivate future extensions to include matter multiplets and generalized-geometry frameworks, as well as potential Calabi–Yau reductions.

Abstract

We explore consistent truncations from 10d/11d supergravity to supergravity theories on brane worldvolumes. Supersymmetric black-brane solutions to these lower-dimensional theories can be uplifted to 10d/11d supergravity and interpreted as intersecting-brane solutions with a particular smearing pattern. We survey this novel family of intersecting-brane solutions which also includes cases that are not related to previously known consistent truncations. Turning the argument on its head, we argue that the knowledge of such solutions allows us to generate appropriate embedding ansätze for consistent truncations. We demonstrate this by deriving new consistent embeddings of pure 5d $\mathcal{N}=4$ supergravity on D4-branes in type IIA theory and of pure 6d $\mathcal{N}=(1,1)$ supergravity on NS5-branes in type IIB theory.