  Branes are ubiquitous elements of any low-energy limit of string theory. We
point out that negative tension branes violate all the standard energy
conditions of the higher-dimensional spacetime they are embedded in; this opens
the door to very peculiar solutions of the higher-dimensional Einstein
equations. Building upon the (3+1)-dimensional implementation of fundamental
string theory, we illustrate the possibilities by considering a toy model
consisting of a (2+1)-dimensional brane propagating through our observable
(3+1)-dimensional universe. Developing a notion of "brane surgery", based on
the Israel--Lanczos--Sen "thin shell" formalism of general relativity, we
analyze the dynamics and find traversable wormholes, closed baby universes,
voids (holes in the spacetime manifold), and an evasion (not a violation) of
both the singularity theorems and the positive mass theorem. These features
appear generic to any D-brane model that permits negative tension branes: This
includes the Randall--Sundrum models and their variants.
