### abstract

- We describe an explicit UV regularization of the brane singularities for all 4D flat configurations of 6D gauged chiral supergravity compactified on axially symmetric internal spaces (for which the general solutions are known). All such solutions have two or fewer co-dimension two singularities, which we resolve in terms of microscopic co-dimension one cylindrical 4-branes, whose interiors are capped using the most general possible 4D flat solution of the 6D field equations. By so doing we show that such a cap is always possible for any given bulk geometry, and obtain an explicit relationship between the properties of the capped 4-branes and the various parameters which describe the bulk solution. We show how these branes generically stabilize the size of the extra dimensions by breaking the scale invariance which relates classical solutions to 6D supergravity, and we compute the scalar potential for this modulus in the 4D effective theory. The lifting of this marginal direction provides a natural realization of the Goldberger-Wise stabilization mechanism in six dimensions.