Branes for Higgs Phases and Exact Conformal Field Theories ∗

We consider multicenter supergravity solutions corresponding to Higgs phases of supersymmetric Yang–Mills theories with ZN symmetric vacuua. In certain energy regimes, we find a description in terms of a generalized wormhole solution that corresponds to the SL(2, IR)/U(1) × SU(2)/U(1) exact conformal field theory. We show that U -dualities map these backgrounds to purely gravitational ones and comment on the relation to the black holes arising from intersecting D1 and D5 branes. We also discuss supersymmetric properties of the various solutions and the relation to 2-dim solitons, on flat space, of the reduced axion-dilaton-gravity equations. Finally, we address the problem of understanding other supergravity solutions from the multicenter ones. As prototype examples we use rotating D3 branes and NS5 and D5 branes associated to non-Abelian duals of 4-dim hyper-Kahler metrics with SO(3) isometry. CERN-TH/98-367 November 1998 ∗ Parts of this paper were presented in talks given at the 32th Ahrenshoop Symposium (BuckowGermany, 1-5 September 1998), the XXI-th Triangle meeting (Kolympari-Greece, 9-12 September 1998) and the 6th Hellenic School and Workshops on Elementary Particle Physics (Corfu-Greece, 6-26 September 1998).