3-branes and uniqueness of the Salam-Sezgin vacuum

We prove the uniqueness of the supersymmetric Salam-Sezgin (Minkowski)(4) X S-2 ground state among all non-singular solutions with a four-dimensional Poincare, de Sitter or anti-de Sitter symmetry. We construct the most general solutions with an axial symmetry in the two-dimensional internal space, and show that included amongst these is a family that is non-singular away from a conical defect at one pole of a distorted 2-sphere. These solutions admit the interpretation of 3-branes with negative tension. (C) 2004 Elsevier B.V. All rights reserved.