Duality twists on a group manifold

We study duality-twisted dimensional reductions on a group manifold G, where the twist is in a group G̃ and examine the conditions for consistency. We find that if the duality twist is introduced through a group element g̃ in G̃, then the flat G̃-connection A = g̃^-1dg̃ must have constant components M_n with respect to the basis 1-forms on G, so that the dependence on the internal coordinates cancels out in the lower dimensional theory. This condition can be satisfied if and only if M_n forms a representation of the Lie algebra of G, which then ensures that the lower dimensional gauge algebra closes. We find the form of this gauge algebra and compare it to that arising from flux compactifications on twisted tori. As an example of our construction, we find a new five dimensional gauged, massive supergravity theory by dimensionally reducing the eight dimensional Type II supergravity on a three dimensional unimodular, non-semi-simple, non-abelian group manifold with an SL(3,ℝ) twist.