Consistent and inconsistent truncations. Some results and the issue of the correct uplifting of solutions

Abstract

We clarify the existence of two different types of truncations of the field content in a theory, the consistency of each type being achieved by different means. A proof is given of the conditions to have a consistent truncation in the case of dimensional reductions induced by independent Killing vectors. We explain in what sense the tracelessness condition found by Scherk and Scharwz is not only a necessary condition but also a {\it sufficient} one for a consistent truncation. The reduction of the gauge group is fully performed showing the existence of a sector of rigid symmetries. We show that truncations originated by the introduction of constraints will in general be inconsistent, but this fact does not prevent the possibility of correct upliftings of solutions in some cases. The presence of constraints has dynamical consequences that turn out to play a fundamental role in the correctness of the uplifting procedure.

Latex, 33 pages, 1 eps fig. v2: typos removed, refs. added

References in corpus (1)

• Consistent Group and Coset Reductions of the Bosonic String

Cited by in corpus (10)

• Double Field Theory on Group Manifolds
• Consistent Compactification of Double Field Theory on Non-geometric Flux Backgrounds
• M-theory and Gauged Supergravities
• The map between conformal hypercomplex/hyper-Kaehler and quaternionic(-Kaehler) geometry
• On the consistency of coset space dimensional reduction
• Truncations driven by constraints: consistency and conditions for correct upliftings
• The dynamics of coset dimensional reduction
• Group Manifold Reduction of Dual N=1 d=10 Supergravity
• Dimensional reduction, truncations, constraints and the issue of consistency
• On static black holes solutions in Einstein and Einstein-Gauss-Bonnet gravity with topology $\mathbf{SO}(\mathbf{n})\times \mathbf{SO}(\mathbf{n})$