FIG. 2: Left: A conformal diagram for AdS$_{4}$ . An S 2 is suppresed at each point except the left vertical line. The coordinates used in Eq. (19) cover the shaded region. Right: The spacetime only exists outside (shaded region) the bubble wall, which respects the de Sitter slicing of AdS$_{4}$ . ∂$_{r}$B ( r ) B ( r ) → H coth( Hr ) rC ( r ) → L (22) in the limit r → ∞ . It is clear from this description that such a solution, if it exists, would have the appropriate asymptotics as r → ∞ to match to the flux compactification solution Eq. (19) at the conformal boundary, where we must additionally impose that the axion θ approach the form Eq. (14). Looking at the boundary conditions imposed above, one can see that the metric in Eq. (20) has the same structure at r → 0 as Witten’s solution discussed previously in Eq. (4); we have a compelling ansatz for a bubble of nothing in this flux compactification. Because the compact dimension in this solution closes smoothly at r = 0, one must introduce some dynamical object that is able to resolve the flux singularity on the surface of the bubble. We can accomplish this simply by examining our original Lagrangian for the complex scalar field in Eq. (7). The problem arises only if one insists on keeping the modulus of the scalar field finite near the surface of the bubble. The divergence of gradient energy is cured by allowing the scalar modulus to relax along the radial direction in such a way that it vanishes at the tip of the cigar-like geometry. This is the same regularization found on a global string (i.e. codimension two) solitonic solution associated with a complex scalar field. 6 Singular bubbles of nothing in AdS$_{5}$ × S $^{5}$/ ❩ k were constructed in [20], yielding a bubble