General matter coupled N=4 gauged supergravity in five dimensions

We construct the general form of matter coupled N = 4 gauged supergravity i n five dimensions. Depending on the structure of the gauge group, these the ories are found to involve vector and/or tensor multiplets. When self-dual tensor fields are present, they must be charged under a one-dimensional Abe lian group and cannot transform non-trivially under any other part of the g auge group. A short analysis of the possible ground states of the different types of theories is given. It is found that AdS ground states are only po ssible when the gauge group is a direct product of a one-dimensional Abelia n group and a semi-simple group. In the purely Abelian, as well as in the p urely semi-simple gauging, at most Minkowski ground states are possible. Th e existence of such Minkowski ground states could be proven in the compact Abelian case. (C) 2001 Elsevier Science B.V. All rights reserved.