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The Thin-Wall Approximation in Vacuum Decay: a Lemma · Around

2017

The Thin-Wall Approximation in Vacuum Decay: a Lemma

Brown, Adam R.

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Understand

The 'thin-wall approximation' gives a simple estimate of the decay rate of an unstable quantum field.

Unfortunately, the approximation is uncontrolled.
In this paper I show that there are actually two different thin-wall approximations and that they bracket the true decay rate: I prove that one is an upper bound and the other a lower bound.
In the thin-wall limit, the two approximations converge.

Built on

T. Banks, C. M. Bender and T. T. Wu, “Coupled anharmonic oscillators. 1. Equal mass case,” Phys. Rev. D 8
1973
Earlier work this paper cites.
S. R. Coleman, “The Fate of the False Vacuum. 1. Semiclassical Theory,” Phys. Rev. D 15
1977
Earlier work this paper cites.
C. G. Callan, Jr. and S. R. Coleman, “The Fate of the False Vacuum. 2. First Quantum Corrections,” Phys. Rev. D 16
1977
Earlier work this paper cites.
S. R. Coleman, V. Glaser, and A. Martin, “Action Minima Among Solutions to a Class of Euclidean Scalar Field Equations,” Commun. Math. Phys. 58 211 (1978)
1978
Earlier work this paper cites.
S. R. Coleman and F. De Luccia, “Gravitational Effects on and of Vacuum Decay,” Phys. Rev. D 21
1980
Earlier work this paper cites.

Similar

S. W. Hawking and I. G. Moss, “Supercooled Phase Transitions in the Very Early Universe,” Phys. Lett. 110B
1982
Cited alongside, same era.
S. R. Coleman, “Quantum Tunneling and Negative Eigenvalues,” Nucl. Phys. B 298
1988
Cited alongside, same era.
S. J. Parke, “Gravity, the Decay of the False Vacuum and the New Inflationary Universe Scenario,” Phys. Lett. 121B
1988
Cited alongside, same era.
D. A. Samuel and W. A. Hiscock, “Effect of gravity on false vacuum decay rates for O(4) symmetric bubble nucleation,” Phys. Rev. D 44
1991
Cited alongside, same era.
U. Gen and M. Sasaki, “False vacuum decay with gravity in nonthin wall limit,” Phys. Rev. D 61
Original
2016
Cited alongside, same era.

Then

D. Garfinkle and R. Gregory, “Corrections to the Thin Wall Approximation in General Relativity,” Phys. Rev. D 41
Original
2016
Later among the works it cites.
H. Ooguri and C. Vafa, “Non-supersymmetric AdS and the Swampland,” arXiv:1610.01533 [hep-th]; B. Freivogel and M. Kleban, “Vacua Morghulis,” arXiv:1610.04564 [hep-th]; U. Danielsson and G. Dibitetto, “Fate of stringy AdS vacua and the weak gravity conjecture,” Phys. Rev. D 96
Original
2017
Closest in time.
D. A. Samuel and W. A. Hiscock, “‘Thin wall’ approximations to vacuum decay rates,” Phys. Lett. B 261
2017
Closest in time.
G. Munster and S. Rotsch, “Analytical calculation of the nucleation rate for first order phase transitions beyond the thin wall approximation,” Eur. Phys. J. C 12
Original
2018
Closest in time.

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