Nonsingular 4d-flat branes in six-dimensional supergravities

We show that six-dimensional supergravity models admit nonsingular solutionsin the presence of flat three-brane sources with positive tensions. The modelsstudied in this paper are nonlinear sigma models with the target spaces of thescalar fields being noncompact manifolds. For the particular solutions of thescalar field equations which we consider, only two brane sources are possiblewhich are positioned at those points where the scalar field densities diverge,without creating a divergence in the Ricci scalar or the total energy. Thesesolutions are locally invariant under 1/2 of D=6 supersymmetries, which,however, do not integrate to global Killing spinors. Other branes can beintroduced by hand by allowing for local deficit angles in the transverse spacewithout generating any kind of curvature singularities.Comment: 13 pages. The discussion of modular invariance is amended and a reference has been adde