Kaluza-Klein supergravity on AdS₃ x S³

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We construct a Chern-Simons type gauged N=8 supergravity in three spacetime dimensions with gauge group SO(4) x T∞ over the infinite dimensional coset space SO(8,∞)/(SO(8) x SO(∞)), where T∞ is an infinite dimensional translation subgroup of SO(8,∞). This theory describes the effective interactions of the (infinitely many) supermultiplets contained in the two spin-1 Kaluza-Klein towers arising in the compactification of N=(2,0) supergravity in six dimensions on AdS₃ x S³ with the massless supergravity multiplet. After the elimination of the gauge fields associated with T∞, one is left with a Yang Mills type gauged supergravity with gauge group SO(4), and in the vacuum the symmetry is broken to the (super-)isometry group of AdS₃ x S³, with infinitely many fields acquiring masses by a variant of the Brout-Englert-Higgs effect.