Truncations driven by constraints: consistency and conditions for correct upliftings

TL;DR

This paper analyzes how constraint-driven truncations in supergravity theories can be consistently uplifted from lower to higher dimensions, providing theorems and examples to ensure correct solution upliftings.

Contribution

It introduces general theorems that establish conditions for the consistent uplift of solutions in constraint-driven truncations, including cases with initially inconsistent truncations.

Findings

Established conditions for correct upliftings in supergravity truncations

Provided examples of upliftings from 7d to 10d supergravity

Demonstrated that some truncations can be correctly uplifted despite initial inconsistencies

Abstract

We discuss the mechanism of truncations driven by the imposition of constraints. We show how the consistency of such truncations is controlled, and give general theorems that establish conditions for the correct uplifting of solutions. We show in some particular examples how one can get correct upliftings from 7d supergravities to 10d type IIB supergravity, even in cases when the truncation is not initially consistent by its own.