GaugedN=4supergravity in six dimensions

We obtain $N=4\mathrm{}$ gauged supergravity in $d=6\mathrm{}$ dimensions from dimensional reduction of $N=2\mathrm{}$, $d=7\mathrm{}$ gauged supergravity. Starting from a topological mass term in the $d=7\mathrm{}$ theory one gets an $N=4\mathrm{}$, $d=6\mathrm{}$ irreducible model with a two-parameter potential and a local SU(2) in which an antisymmetric rank-two tensor absorbs a Higgs-vector field and becomes massive. Without a topological mass term in $d=7\mathrm{}$ we get the reducible coupling of pure gauged $N=4\mathrm{}$ supergravity to a vector multiplet. We also consider various truncations to matter-coupled $N=2\mathrm{}$ theories. The pure gauged $N=4\mathrm{}$ supergravity gauges the superalgebra $F_4$.