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

TL;DR

This work addresses the problem of finding fully consistent sphere reductions that retain the complete $SO(n+1)$ Yang-Mills sector in lower-dimensional supergravities. The authors construct a consistent $S^3$ reduction of type IIA supergravity to seven dimensions, with a maximal gauged supergravity having $SO(4)$ gauge fields, by exploiting a singular limit of the known $S^4$ reduction of $D=11$ supergravity that degenerates the internal sphere to $\mathbb{R}\times S^3$. They also obtain the $S^4$ reduction of type IIA, which yields an $SO(5)$-gauged maximal supergravity in $D=6$, by performing a standard $S^1$ reduction of the $D=7$ $SO(5)$ gauged theory and reinterpreting the result. These constructions extend the set of explicit, consistent Kaluza–Klein reductions and pave the way for domain-wall/QFT applications, highlighting that such reductions can exist even when there is no conventional group-theoretic justification.

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.