Yang-Mills<i>–</i>Einstein supergravity in seven dimensions

Abstract

We construct couplings of n vector multiplets to seven-dimensional N=2 supergravity. The 3n scalars of the theory parametrize the coset SO(n,3)/SO(n)\ifmmode\times\else\texttimes\fi{}SO(3). The (n+3) vector fields are used to gauge either an SO(3)\ifmmode\times\else\texttimes\fi{}H (dimension H=n) or an SO(3,1)\ifmmode\times\else\texttimes\fi{}H (dim H=n-3) subgroup of SO(n,3). The theory has an indefinite potential which triggers compactification into (Minkowski${)}_{4}$\ifmmode\times\else\texttimes\fi{}${\mathrm{S}}^{3}$, with surviving N=1 supersymmetry.