[Paper Review] Vacua Morghulis

Ben Freivogel, Matthew Kleban|arXiv (Cornell University)|Oct 14, 2016

Sports and Physical Education Research22 citations

TL;DR

The paper conjectures that all vacua in string theory are unstable: non-supersymmetric vacua decay metastably, while supersymmetric vacua are marginally unstable via domain walls saturating a tension bound. This implies that arbitrarily large regions of lower-energy vacua can be embedded in higher-energy spacetimes, especially in de Sitter and anti-de Sitter settings, with decay processes occurring on scales much smaller than the horizon when the cosmological constant is small.

ABSTRACT

We conjecture that all vacua in string theory decay. More precisely, non-supersymmetric vacua in string theory are at most metastable and eventually decay, while supersymmetric vacua are only marginally stable. All de Sitter vacua with small cosmological constant are metastable to decay via a process that occurs on scales small compared to the horizon size.

Motivation & Objective

• To propose a universal instability bound for all vacua in string theory, extending the weak gravity conjecture to vacuum decay.
• To resolve the tension between perturbatively stable vacua and the requirement that no non-supersymmetric vacuum be absolutely stable.
• To explore the consequences of vacuum decay for the structure of the string theory landscape, particularly in de Sitter and anti-de Sitter spacetimes.
• To demonstrate that marginally stable vacua allow for arbitrarily large true vacuum regions in false vacuum spacetimes via flat domain walls.
• To argue that de Sitter vacua with small cosmological constants decay on scales much smaller than the horizon, persisting in the zero-Λ limit.

Proposed method

• Use of dualization between scalar fields and fluxes to map domain walls to charged branes, enabling application of the weak gravity conjecture to vacuum decay.
• Application of the BPS bound on domain wall tension, comparing it to the stability bound derived from Einstein equations and instanton decay rates.
• Analysis of thin-wall solutions in AdS and de Sitter spacetimes using Israel junction conditions to relate extrinsic curvature discontinuity to domain wall tension.
• Derivation of the mass scaling of spherical domain walls in the large-radius limit, showing that negative mass at leading order implies instability and bubble expansion.
• Use of the critical tension condition $ T = 2(1/ ho_T - 1/ ho_F) $ to identify the threshold where mass per unit area vanishes in the large-size limit.
• Comparison of decay rates in the limit of small cosmological constant, showing persistence of decay channels below the 'great divide' in the landscape.

Experimental results

Research questions

• RQ1 Can all non-supersymmetric vacua in string theory be at most metastable, with no absolutely stable configurations?
• RQ2 Do supersymmetric vacua always connect to other vacua via BPS-saturating domain walls, and what are the implications for embedding lower-energy vacua?
• RQ3 Can arbitrarily large regions of a lower-energy vacuum be embedded in a higher-energy false vacuum spacetime, and under what conditions?
• RQ4 Does vacuum decay in de Sitter spacetimes with small cosmological constant occur on scales much smaller than the horizon size?
• RQ5 Is the decay of de Sitter vacua stable in the limit where the cosmological constant approaches zero, implying they lie below the 'great divide'?

Key findings

• Non-supersymmetric Minkowski and AdS vacua are at most metastable, decaying via bubble nucleation with a rate faster than the Poincaré recurrence time.
• Supersymmetric vacua are marginally unstable, connected to other vacua by domain walls that saturate the BPS tension bound, allowing flat domain walls to interpolate between vacua.
• In the critical case where domain wall tension saturates the stability bound, the mass per unit area of a large spherical bubble of true vacuum approaches zero, enabling arbitrarily large true vacuum regions in false vacuum spacetimes.
• For de Sitter vacua with small cosmological constant, decay occurs on scales much smaller than the horizon size, and the decay process persists in the limit Λ → 0, placing such vacua below the 'great divide'.
• The thin-wall solution with vanishing mass per unit area in the large-size limit confirms that marginally stable vacua allow for the construction of macroscopic true vacuum regions within false vacuum spacetimes.
• The analysis shows that the weak gravity conjecture, when dualized to domain walls, provides an upper bound on instanton action, suggesting a universal mechanism for vacuum decay in string theory.