# Embedding the SU(3) sector of SO(8) supergravity in $D=11$

## TL;DR

This paper constructs an explicit uplift of the SU(3)--invariant sector of four-dimensional maximal supergravity with SO(8) gauging to eleven-dimensional supergravity, including new consistent truncations and detailed tensor analysis.

## Contribution

It provides the first explicit embedding of the SU(3) sector into D=11 supergravity, extending previous truncations and introducing a new minimal N=2 gauged supergravity truncation.

## Key findings

- Explicit D=11 uplift of SU(3) sector achieved.
- New consistent truncation to minimal N=2 supergravity found.
- Unified framework for known and new truncations developed.

## Abstract

The SU(3)--invariant sector of maximal supergravity in four dimensions with an SO(8) gauging is uplifted to $D=11$ supergravity. In order to do this, the SU(3)--neutral sector of the tensor and duality hierarchies of the $D=4$ ${\cal N}=8$ supergravity is first worked out. The consistent $D=11$ embedding of the full, dynamical SU(3) sector is then expressed at the level of the $D=11$ metric and three-form gauge field in terms of these $D=4$ tensors. The redundancies introduced by this approach are eliminated at the level of the $D=11$ four-form field strength by making use of the $D=4$ duality hierarchy. Our results encompass previously known truncations of $D=11$ supergravity down to sectors of SO(8) supergravity with symmetry larger than SU(3), and include new ones. In particular, we obtain a new consistent truncation of $D=11$ supergravity to minimal $D=4$ ${\cal N}=2$ gauged supergravity.