S^3 and S^4 Reductions of Type IIA Supergravity

TL;DR

This paper develops consistent reductions of type IIA supergravity on S^3 and S^4, leading to new gauged supergravity theories in seven and six dimensions through singular limits of known higher-dimensional reductions.

Contribution

It introduces a novel S^3 reduction of type IIA supergravity and reinterprets a limit of S^4 reduction as an S^3 reduction, expanding the landscape of consistent supergravity reductions.

Findings

Constructed a consistent S^3 reduction of type IIA supergravity.

Derived an S^4 reduction of type IIA supergravity leading to SO(5)-gauged supergravity.

Reinterpreted a singular limit of S^4 reduction as an S^3 reduction of type IIA.

Abstract

We construct a consistent reduction of type IIA supergravity on S^3, leading to a maximal gauged supergravity in seven dimensions with the full set of massless SO(4) Yang-Mills fields. We do this by starting with the known S^4 reduction of eleven-dimensional supergravity, and showing that it is possible to take a singular limit of the resulting standard SO(5)-gauged maximal supergravity in seven dimensions, whose eleven-dimensional interpretation involves taking a limit where the internal 4-sphere degenerates to RxS^3. This allows us to reinterpret the limiting SO(4)-gauged theory in seven dimensions as the S^3 reduction of type IIA supergravity. We also obtain the consistent S^4 reduction of type IIA supergravity, which gives an SO(5)-gauged maximal supergravity in D=6.