Morse-Bott inequalities yield homology bounds and topology-change counts for generic cobordisms to nothing in string theory compactifications.
Decay of flux vacua to nothing
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abstract
We construct instanton solutions describing the decay of flux compactifications of a $6d$ gauge theory by generalizing the Kaluza-Klein bubble of nothing. The surface of the bubble is described by a smooth magnetically charged solitonic brane whose asymptotic flux is precisely that responsible for stabilizing the 4d compactification. We describe several instances of bubble geometries for the various vacua occurring in a $6d$ Einstein-Maxwell theory namely, AdS_4 x S^2, R^{1,3} x S^2, and dS_4 x S^2. Unlike conventional solutions, the bubbles of nothing introduced here occur where a {\em two}-sphere compactification manifold homogeneously degenerates.
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Morse-Bott inequalities, Topology Change and Cobordisms to Nothing
Morse-Bott inequalities yield homology bounds and topology-change counts for generic cobordisms to nothing in string theory compactifications.
- Bordisms between 9d type IIB supergravities and commutator widths of duality groups