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.
Highlights
Being complicated theories with large field contents, it proves useful for applications to truncate maximal gauged supergravities to smaller subsectors that are invariant under some symmetry group
The goal of this paper is to provide the consistent uplift of the SU(3) sector of SO(8) gauged supergravity into D 1⁄4 11 by using the uplifting formulas of [25], putting them to the test
Expressing the D 1⁄4 11 embedding at the level of the four-form field strength and employing these D 1⁄4 4 dualizations, redundancy-free uplifting formulas are obtained that contain only the dynamically independent fields that feature in the conventional D 1⁄4 4 N 1⁄4 8 Lagrangian
Summary
Being complicated theories with large field contents, it proves useful for applications to truncate maximal gauged supergravities to smaller subsectors that are invariant under some symmetry group. A systematic approach to the consistent uplift of D 1⁄4 4 N 1⁄4 8 SO(8) supergravity to D 1⁄4 11 was proposed in [25], similar to the method employed in [29,30] to uplift D 1⁄4 4 N 1⁄4 8 ISO(7) supergravity [31] into type IIA This approach relies on the tensor hierachy [32,33] of maximal four-dimensional supergravity—the extension of its field content to include the magnetic gauge fields along with higher rank potentials in representations of E7ð7Þ. Expressing the D 1⁄4 11 embedding at the level of the four-form field strength and employing these D 1⁄4 4 dualizations, redundancy-free uplifting formulas are obtained that contain only the dynamically independent fields (that is, the metric, the scalars and the electric vectors) that feature in the conventional D 1⁄4 4 N 1⁄4 8 Lagrangian. Contact with the consistent uplift of previously known subsectors is made and a new D 1⁄4 11 embedding of D 1⁄4 4 N 1⁄4 2 pure gauged supergravity is established.
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