Cobordism and bubbles of anything in the string landscape

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 S1 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.

Bubbles of nothing: the tunneling potential approach

“…Applying a V t approach to their description seems possible and our first explorations look rather promising. Indeed, we find that the V t description of Witten's BoNs with defects [21,54] is rather straightforward via a simple rescaling of the prefactor of Witten's BoN in (3.22) to take into account the deficit angle associated to the singular behaviour of the BoN. It would be interesting to see how this generalizes in the presence of a nonzero potential for the modulus field.…”

“…Finally, we have not found a higher dimensional interpretation for type − * solutions. Nevertheless, we do not discard type − * and + BoN solutions as they might be relevant to describe bubbles of nothing with defects or compact geometries more complicated than spheres (like Calabi-Yau orientifolds) shrinking to zero through a defect [54].…”

“…The bottom-up analysis, therefore, motivates the question: what are the possible geometries of the compactified space (or field content in the effective 4d theory) that can realize BoN solutions of types + or − * [or type − with a 2 ̸ = (d + 2)/(3d)]? A different avenue to realise these more exotic type of solutions would be to embrace the possibility of singular BoNs (see [26,57,58] and, more recently, [54]). Indeed, the presence of a singularity might be signalling the need to dress the BoN with a brane, or another UV object, whose properties (tension and charge) could be inferred from the behaviour of the solution in the limit ϕ → ∞.…”

The bubble of nothing under T-duality

“…Being a simple solution to Einstein's equations in the vacuum, it has been generalized (see e.g. [2][3][4][5]) and studied in various contexts. In recent years, it has played a prominent role in understanding the stability of non-supersymmetric vacua in string theory [6][7][8][9][10][11].…”

“…These solutions describing dynamical cobordisms to nothing JHEP05(2024)333 were introduced in [22] and further explored in [23] (see also [24][25][26][27][28]). 1 The BoN serves as one of the simplest examples of such dynamical realizations of cobordisms to nothing (for related work on the bubble of nothing in the context of the cobordism conjecture, see [5]). One of the original motivations for this work was to understand how dynamical realizations of cobordisms to nothing behave under T-duality.…”