document: We prove the uniqueness of the supersymmetric Salam–Sezgin (Minkowski)4×S2 ground state among all non-singular solutions with a four-dimensional Poincaré, 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.
extractive_keyphrases: construct the most general solutions prove the uniqueness
abstractive_keyphrases: 3-branes with negative tension axial symmetry in the two-dimensional internal space, de sitter or anti-de sitter symmetry interpretation of 3-branes with negative tension non-singular away from a conical defect non-singular solutions with a four-dimensional poincaré