D=7 SU(2) Gauged Supergravity From D=10 Supergravity

TL;DR

The paper derives a seven-dimensional $SU(2)$-gauged supergravity by compactifying ten-dimensional $N=1$ supergravity on the group manifold $SU(2)$. It presents a concrete Scherk–Schwarz reduction, reduces the bosonic sector to a seven-dimensional Lagrangian ${\cal L}_{7}$ with gauge and antisymmetric tensor fields, and demonstrates that it reproduces the known $D=7$, $N=2$, $SU(2)$ gauged supergravity of Townsend and van Nieuwenhuizen after suitable identifications and a duality between a 3-form and a 2-form. It also discusses the relation to eleven-dimensional reductions and consistency checks in the fermionic sector. This work strengthensthe link between high-dimensional supergravities and lower-dimensional gauged theories, with implications for nonlinear Kaluza–Klein reductions and AdS/CFT contexts.

Abstract

The theory of SU(2) gauged seven-dimensional supergravity is obtained by compactifying ten dimensional N=1 supergravity on the group manifold SU(2).