Abstract
We discuss consistent truncations of eleven-dimensional supergravity on a six-dimensional manifold M, preserving minimal mathcal{N} = 2 supersymmetry in five dimensions. These are based on GS ⊆ USp(6) structures for the generalised E6(6) tangent bundle on M, such that the intrinsic torsion is a constant GS singlet. We spell out the algorithm defining the full bosonic truncation ansatz and then apply this formalism to consistent truncations that contain warped AdS5×wM solutions arising from M5-branes wrapped on a Riemann surface. The generalised U(1) structure associated with the mathcal{N} = 2 solution of Maldacena-Nuñez leads to five-dimensional supergravity with four vector multiplets, one hypermultiplet and SO(3) × U(1) × ℝ gauge group. The generalised structure associated with “BBBW” solutions yields two vector multiplets, one hypermultiplet and an abelian gauging. We argue that these are the most general consistent truncations on such backgrounds.
Highlights
Consistent Kaluza-Klein truncations are a precious tool for constructing compactifying solutions to ten or eleven-dimensional supergravity using a simpler lower-dimensional theory.Given a splitting of the higher-dimensional spacetime into an internal manifold M and an external spacetime X, a consistent truncation selects a finite subset of the KK modes of the higher-dimensional theory on M and provides an effective theory on X describing their non-linear dynamics
We spell out the algorithm defining the full bosonic truncation ansatz and apply this formalism to consistent truncations that contain warped AdS5 ×w M solutions arising from M5-branes wrapped on a Riemann surface
We start with the N = 2 background of Maldacena-Nuñez [34]: specifying its U (1)S generalised structure and discussing its singlet intrinsic torsion, we obtain a consistent truncation to five-dimensional N = 2 supergravity including four vector multiplets, one hypermultiplet, and a non-abelian SO(3) × U (1) × R gauging
Summary
Consistent Kaluza-Klein truncations are a precious tool for constructing compactifying solutions to ten or eleven-dimensional supergravity using a simpler lower-dimensional theory. We start with the N = 2 background of Maldacena-Nuñez [34]: specifying its U (1)S generalised structure and discussing its singlet intrinsic torsion, we obtain a consistent truncation to five-dimensional N = 2 supergravity including four vector multiplets, one hypermultiplet, and a non-abelian SO(3) × U (1) × R gauging. This extends the abelian truncation of [36] (see [10, 37] for previous subtruncations) by adding SO(3) vector multiplets, which in the dual superconformal field theory source SO(3) flavour current multiplets. A more extended review of the relevant generalised geometry can be found in appendix A
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