Abstract
A bubble of nothing is a spacetime instability where a compact dimension collapses. After nucleation, it expands at the speed of light, leaving “nothing” behind. We argue that the topological and dynamical mechanisms which could protect a compactification against decay to nothing seem to be absent in string compactifications once supersymmetry is broken. The topological obstruction lies in a bordism group and, surprisingly, it can disappear even for a SUSY-compatible spin structure. As a proof of principle, we construct an explicit bubble of nothing for a T3 with completely periodic (SUSY-compatible) spin structure in an Einstein dilaton Gauss-Bonnet theory, which arises in the low-energy limit of certain heterotic and type II flux compactifications. Without the topological protection, supersymmetric compactifications are purely stabilized by a Coleman-deLuccia mechanism, which relies on a certain local energy condition. This is violated in our example by the nonsupersymmetric GB term. In the presence of fluxes this energy condition gets modified and its violation might be related to the Weak Gravity Conjecture.We expect that our techniques can be used to construct a plethora of new bubbles of nothing in any setup where the low-energy bordism group vanishes, including type II compactifications on CY3, AdS flux compactifications on 5-manifolds, and M-theory on 7-manifolds. This lends further evidence to the conjecture that any non-supersymmetric vacuum of quantum gravity is ultimately unstable.
Highlights
It is known that non-supersymmetric vacua typically exhibit instabilities, either at the perturbative or non-perturbative level
We argue that the topological and dynamical mechanisms which could protect a compactification against decay to nothing seem to be absent in string compactifications once supersymmetry is broken
Can we ensure that this is a necessary implication of breaking supersymmetry? Is it consistent to have a non-supersymmetric stable vacuum? In [1, 2] it was conjectured that any non-supersymmetric vacuum of a consistent theory of quantum gravity is unstable
Summary
It is known that non-supersymmetric vacua typically exhibit instabilities, either at the perturbative or non-perturbative level. For the first time in the literature we will explicitly construct bubbles of nothing compatible with supersymmetric boundary conditions, and which do not require an ad hoc gauge coupling for the fermions This opens up a new type of decay mode that might be universally present even if supersymmetry is only broken at low energies. Recall that ΩS3pin = 0, implying that the bubble of nothing can be constructed completely within the framework of the (D-dimensional) low-energy effective field theory, without the need of invoking exotic UV ingredients This will make easier to construct smooth solutions such that the semi-classical description of the decay is justified. As a supersymmetry breaking source, the theory includes a Gauss-Bonnet higher derivative term, which will violate the dominant energy condition, allowing us to construct bubble solutions with a non-vanishing vacuum decay rate. It is straightforward to adapt our results to obtain an explicit geometric description of flux compactifications on a warped K3 manifold
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