3-Branes and Uniqueness of the Salam-Sezgin Vacuum

TL;DR

The paper proves that the supersymmetric Salam-Sezgin ground state $({\rm Minkowski})_4\times S^2$ is the unique nonsingular background with a compact internal space and four-dimensionally maximal symmetry in the six-dimensional gauged supergravity model. By deriving and solving the axisymmetric equations for the internal space, it shows that the only completely regular solution is the Salam-Sezgin vacuum; other axisymmetric configurations yield conical defects interpretable as 3-branes, typically with negative tension due to Dirac quantization. The work further explores the inclusion of additional gauge fields, the resulting brane/flux constraints, and the dilaton coupling, arguing a vanishing brane-dilaton coupling is consistent with regular solutions. It also analyzes a modulus and a breathing radion mode, deriving the 4D effective potential and radion mass, thereby clarifying the light degrees of freedom in this compactification and its implications for phenomenology.

Abstract

We prove the uniqueness of the supersymmetric Salam-Sezgin (Minkowski)_4\times S^2 ground state among all nonsingular 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.