Abstract
We investigate the non-perturbative stability of supersymmetric compactifications with respect to decay via a bubble of nothing. We show examples where this kind of instability is not prohibited by the spin structure, i.e., periodicity of fermions about the extra dimension. However, such ``topologically unobstructed'' cases do exhibit an extra-dimensional analog of the well-known Coleman-De Luccia suppression mechanism, which prohibits the decay of supersymmetric vacua. We demonstrate this explicitly in a four dimensional Abelian-Higgs toy model coupled to supergravity. The compactification of this model to M3 × S1 presents the possibility of vacua with different windings for the scalar field. Away from the supersymmetric limit, these states decay by the formation of a bubble of nothing, dressed with an Abelian-Higgs vortex. We show how, as one approaches the supersymmetric limit, the circumference of the topologically unobstructed bubble becomes infinite, thereby preventing the realization of this decay. This demonstrates the dynamical origin of the decay suppression, as opposed to the more familiar argument based on the spin structure. We conjecture that this is a generic mechanism that enforces stability of any topologically unobstructed supersymmetric compactification.
Highlights
Observations is one of the major challenges facing all fundamental higher dimensional theories, such as String Theory
Supersymmetry imposes a lower bound on the tension of the wall interpolating between supersymmetric vacua, so it is clear that the bubble decay process cannot occur if this lower bound on tension is at or above the tension corresponding to an infinite critical radius
It is generally believed that supersymmetric compactifications would be stable with respect to this decay channel due to the necessity of periodic fermions around the extra dimension
Summary
As we mentioned in the introduction, we would like to study a model whose compactification on a circle allows for anti-periodic fermionic boundary conditions, while still preserving part of its supersymmetry. We will show in this paper that we can find a compactification with these characteristics within the Abelian-Higgs model coupled to N = 1 supergravity in 3 + 1 dimensions.. The full supergravity model involves the gravitino field, ψμ, and the fermionic partners of the chiral and gauge fields, χ and λ, respectively.5 Note that the combination ξ ≡ eη appearing in the scalar potential contributes to the charge of all fermions under the local U(1) symmetry Such a combination can be identified as the Fayet-Iliopoulos (FI) term of N = 1 supergravity, and it is associated to the gauging of the R−symmetry which rotates the supercharges.
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