Bubbles of Nothing and Supersymmetric Compactifications

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 $M_3\times S_1$ 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.

33 pages, 9 figures

References in corpus (3)

• Quantization of Fayet-Iliopoulos Parameters in Supergravity
• Bubbles of Nothing in Flux Compactifications
• Decay of flux vacua to nothing

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• Looking for structure in the cobordism conjecture
• Bubble of nothing decays of unstable theories
• de Sitter Decays to Infinity
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• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• Waves in the Witten Bubble of Nothing and the Hawking Wormhole
• Morse-Bott inequalities, Topology Change and Cobordisms to Nothing