Tri-Sasakian consistent reduction

TL;DR

This paper develops a universal consistent Kaluza-Klein truncation of M-theory on tri-Sasakian manifolds, resulting in a four-dimensional N=4 gauged supergravity with specific gauge groups and symmetry properties.

Contribution

It introduces a universal consistent truncation based on tri-Sasakian structures, connecting it with exceptional geometry and providing various subtruncations and vacuum solutions.

Findings

Constructed a consistent truncation leading to N=4 gauged supergravity.

Embedded the symmetry groups within E7(7) and linked with Exceptional Generalized Geometry.

Identified vacuum solutions with different supersymmetry breaking patterns.

Abstract

We establish a universal consistent Kaluza-Klein truncation of M-theory based on seven-dimensional tri-Sasakian structure. The four-dimensional truncated theory is an N=4 gauged supergravity with three vector multiplets and a non-abelian gauge group, containing the compact factor SO(3). Consistency follows from the fact that our truncation takes exactly the same form as a left-invariant reduction on a specific coset manifold, and we show that the same holds for the various universal consistent truncations recently put forward in the literature. We describe how the global symmetry group SL(2,R) x SO(6,3) is embedded in the symmetry group E7(7) of maximally supersymmetric reductions, and make the connection with the approach of Exceptional Generalized Geometry. Vacuum AdS4 solutions spontaneously break the amount of supersymmetry from N=4 to N=3,1 or 0, and the spectrum contains massive modes. We find a subtruncation to minimal N=3 gauged supergravity as well as an N=1 subtruncation to the SO(3)-invariant sector. We also show that a reduction on the homogeneous space N^{010} enhances the universal tri-Sasakian truncation with a Betti vector multiplet.