Cobordism and Bubbles of Anything in the String Landscape

TL;DR

The work develops a 4d EFT framework to model bubble of nothing and bubble of something processes in string landscapes, employing ETW boundaries realized by defects with size $\eta$ and deficit angle $\theta$ in both simple Witten-type setups and Calabi–Yau orientifolds. It derives explicit decay/creation exponents that depend on the defect data and wall tension, and extends the analysis to Type IIB realizations with O3/O7/O5 planes, where the ETW brane is realized by an O5/D5 system. The authors connect these wall data to CY compactifications, including CY shrinking scenarios, and compare to existing results, validating the 4d EFT approach and highlighting how SUSY breaking, fluxes, and potentials modify rates. They also discuss the interpretation of “nothing” as AdS in certain limits and outline how to refine the estimates with nontrivial potentials, fluxes, and higher-order corrections. Overall, the paper provides a cohesive toolkit for assessing the stability and transitions among string vacua via bubbles of nothing or something and identifies key levers—defect size, deficit angle, and wall tension—that control the landscape dynamics and their phenomenological implications.

Abstract

We study bubble of nothing decays and their reverse processes, the creation of vacua through `bubbles of something', in models of the Universe based on string theory. From the four-dimensional perspective, the corresponding gravitational instantons contain an end-of-the-world (ETW) boundary or brane, realized by the internal manifold shrinking to zero size. The existence of such ETW branes is predicted by the Cobordism Conjecture. We develop the 4d EFT description of such boundaries at three levels: First, by generalizing the Witten bubble through an additional defect. Second, by replacing the compact $S^1$ with a Calabi-Yau orientifold and allowing it to shrink and disappear through a postulated defect. Third, we describe an ETW brane construction for type IIB Calabi-Yau orientifold compactifications with O3/O7 planes through an appropriate additional O5 orientifolding. Our 4d EFT formalism allows us to compute the decay/creation rates for bubbles of anything depending on two parameters: The size of the relevant defect and its tension a.k.a. the induced (generalized) deficit angle.

Figures (7)

• Figure 1: Illustration of the bubble of nothing (left) and the bubble of something (right) instanton. In both cases, the four-dimensional space $\mathcal{M}$ has a spherical boundary which coincides with the locus where the internal manifold, shown above $\mathcal{M}$, shrinks to zero size.
• Figure 2: Physical processes corresponding to bubble of nothing (left) and bubble of something (right). The dashed line denotes the locus of analytic continuation from euclidean half instanton to the Lorentzian, expanding bubble. The solid black line is the boundary of 4d space.
• Figure 3: A bordism between $S^1$ and nothing, including a defect (drawn as a red disk).
• Figure 4: Instantons for a bubble of nothing decay (left) and a decay to AdS (right) of Minkowski space. In the second case, the ball of AdS glued into the flat space ${\cal M}$ has most of its contribution to the action localized near the boundary, here illustrated by the blue-shaded region.
• Figure 5: We display the Penrose diagram for a Minkowski bubble of nothing (left) and a Minkowski to AdS decay (right). On the left, the red line denotes the ETW brane. On the right, the blue lines characterize the AdS region and the red line represents the domain wall. In both diagrams, the dashed line denotes the quantum process of the critical bubble emerging. The ETW brane on the left requires a negative tension while the domain wall on the right has positive tension.