Metastability and Vacuum Decay

Metastable vacuum decay is not determined by a barrier height alone. A rate claim requires a false-vacuum persistence observable, a finite-action bounce with return-to-false-vacuum boundary conditions, the correct instability and zero modes, a renormalized prefactor, and quantitative control of approximations and environmental effects. This chapter develops that chain in flat spacetime at zero temperature and gives exact transfers when multifield geometry, thermal physics, or gravity changes the problem.

Enter this chapter

Begin with Bounce Solutions and False-Vacuum Boundary Conditions to construct a saddle that returns to the false vacuum at Euclidean infinity.

Helpful background. Review What an Interacting Lagrangian Does and Does Not Specify and Cross Sections and Decay Rates for the limits of a classical potential and the meaning of a decay rate.

Topics

1. Bounce Solutions and False-Vacuum Boundary Conditions — Imposes the bounce’s regularity and asymptotic conditions.
2. Decay Rates, the Negative Mode, and Prefactors — Connects unstable and translation modes to the decay prefactor.
3. Bounce Existence, Symmetry, and Multifield Geometry — Checks existence and the role of multifield trajectories.
4. Thin-Wall Control and Beyond-Thin-Wall Corrections — Controls the separation between bubble radius and wall thickness.
5. Gauge and Renormalization-Scale Dependence of Decay Rates — Combines gauge- and scale-dependent pieces into a physical rate.
6. Validity Limits, Thermal Effects, and Gravity — Identifies when thermal or gravitational effects change the problem.

How the ideas fit together

An instanton between degenerate minima and a false-vacuum bounce have different boundary conditions and physical meanings. The bounce returns to the same false vacuum and has the instability needed to produce a decay contribution on the false-vacuum contour. Its action controls the leading exponential, while zero modes and the renormalized determinant supply the rate’s dimensions and normalization. A barrier height or bounce action alone is therefore insufficient; thin-wall and loop approximations must also remain controlled. Callan and Coleman 1977, pp. 1762–1768.

Where to go next

Continue to Strong-Coupling Laboratories and Dual Variables to determine how target geometry and spacetime dimension constrain a sigma model.

References

• Callan, Curtis G., Jr., and Sidney Coleman. “Fate of the False Vacuum. II. First Quantum Corrections.” Physical Review D 16 (1977): 1762–1768. DOI.