Fluctuations about the Fubini-Lipatov instanton for false vacuum decay in classically scale invariant models

Garbrecht, Björn; Millington, Peter

doi:10.1103/physrevd.98.016001

Cited by 13 publications

(21 citation statements)

References 44 publications

(108 reference statements)

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“…This problem applies to situations where the scale of the nucleated bubble depends on radiative effects, i.e. as occurs in approximately scale invariant theories such as the SM [22,23,41], but also when the true vacuum only emerges radiatively in the first place through, e.g., the Coleman-Weinberg mechanism [42][43][44][45]. Furthermore, evaluating the functional determinant using the Gel'fand-Yaglom theorem does not lead to a systematic method of computing higher-order corrections.…”

Section: Introductionmentioning

confidence: 99%

Radiative effects on false vacuum decay in Higgs-Yukawa theory

Garbrecht

Millington

2018

Phys. Rev. D

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We derive fermionic Green's functions in the background of the Euclidean solitons describing false vacuum decay in a prototypal Higgs-Yukawa theory. In combination with appropriate counterterms for the masses, couplings and wave-function normalization, these can be used to calculate radiative corrections to the soliton solutions and transition rates that fully account for the inhomogeneous background provided by the nucleated bubble. We apply this approach to the archetypal example of transitions between the quasi-degenerate vacua of a massive scalar field with a quartic selfinteraction. The effect of fermion loops is compared with those from additional scalar fields, and the loop effects accounting for the spacetime inhomogeneity of the tunneling configuration are compared with those where gradients are neglected. We find that scalar loops lead to an enhancement of the decay rate, whereas fermion loops lead to a suppression. These effects get relatively amplified by a perturbatively small factor when gradients are accounted for. In addition, we observe that the radiative corrections to the solitonic field profiles are smoother when the gradients are included. The method presented here for computing fermionic radiative corrections should be applicable beyond the archetypal example of vacuum decay. In particular, we work out methods that are suitable for calculations in the thin-wall limit, as well as others that take account of the full spherical symmetry of the solution. For the latter case, we construct the Green's functions based on spin hyperspherical harmonics, which are eigenfunctions of the appropriate angular momentum operators that commute with the Dirac operator in the solitonic background.

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Section: Introductionmentioning

confidence: 99%

Radiative effects on false vacuum decay in Higgs-Yukawa theory

Garbrecht

Millington

2018

Phys. Rev. D

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“…Ref. [39] for an extensive discussion of the Fubini-Lipatov instanton, which is perhaps the simplest example with spherical geometry and where only the Green's function but not the spectrum is known analytically). For these reasons, we also use the archetypical model in order to exemplify the analytic continuation of the modes and the spectrum in the upcoming section.…”

Section: Spherical Geometrymentioning

confidence: 99%

“…Further, there are two discrete eigenvalues corresponding to = 1 (with a positive eigenvalue λ = 3γ 2 ) and = 2 (giving a zero mode, associated with time translations) [34,39,42]. (For the thin-wall problem, there are two discrete modes for each k.) There is no negative mode because the kink is not a true bounce or tunneling solution (which should tend to the false vacuum both at τ → ±∞, while the kink only does so only at positive infinity).…”

Section: Fluctuation Spectrum About An Instanton In the Double-well Pmentioning

confidence: 99%

“…This equation has been solved analytically in Refs. [34,39]. Moreover, since the spectrum of the kink is known, as discussed in Section 5.2, the Green's function can be decomposed into contributions from the discrete and continuum spectrum, respectively [39].…”

Section: B3 Application To the Kink Backgroundmentioning

confidence: 99%

“…The main advantage of the resolvent method therefore appears to be that the Green's function can readily be employed in order to compute e.g. corrections to the bounce [34,37,38] and other one-loop resummed [39] or higher-order quantities [40,41]. Both approaches avoid the direct solution for the spectrum that has been used in Section 5.3.…”

Section: B4 Utility Of the Different Approachesmentioning

confidence: 99%

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Functional methods for false-vacuum decay in real time

Garbrecht

Tamarit

2019

J. High Energ. Phys.

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We present the calculation of the Feynman path integral in real time for tunneling in quantum mechanics and field theory, including the first quantum corrections. For this purpose, we use the well-known fact that Euclidean saddle points in terms of real fields can be analytically continued to complex saddles of the action in Minkowski space. We also use Picard-Lefschetz theory in order to determine the middle-dimensional steepest-descent surface in the complex field space, constructed from Lefschetz thimbles, on which the path integral is to be performed. As an alternative to extracting the decay rate from the imaginary part of the ground-state energy of the false vacuum, we use the optical theorem in order to derive it from the real-time amplitude for forward scattering. While this amplitude may in principle be obtained by analytic continuation of its Euclidean counterpart, we work out in detail how it can be computed to one-loop order at the level of the path integral, i.e. evaluating the Gaußian integrals of fluctuations about the relevant complex saddle points. To that effect, we show how the eigenvalues and eigenfunctions on a thimble can be obtained by analytic continuation of the Euclidean eigensystem, and we determine the path-integral measure on thimbles. This way, using real-time methods, we recover the one-loop result by Callan and Coleman for the decay rate. As a byproduct of our derivation, we note that the optical theorem suggests an interpretation of the false-vacuum energy in flat space in terms of the normalization of the position or field eigenstate associated with the false vacuum, with unit norm corresponding to zero energy up to volume-suppressed effects. We finally demonstrate our real-time methods explicitly, including the construction of the eigensystem of the complex saddle, on the archetypical example of tunneling in a quasi-degenerate quartic potential. arXiv:1905.04236v1 [hep-th]

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Double-well instantons in finite volume

Ai,

Alexandre,

Carosi

et al. 2024

J. High Energ. Phys.

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Assuming a toroidal space with finite volume, we derive analytically the full one-loop vacuum energy for a scalar field tunnelling between two degenerate vacua, taking into account discrete momentum. The Casimir energy is computed for an arbitrary number of dimensions using the Abel-Plana formula, while the one-loop instanton functional determinant is evaluated using the Green’s functions for the fluctuation operators. The resulting energetic properties are non-trivial: both the Casimir effect and tunnelling contribute to the Null Energy Condition violation, arising from a non-extensive true vacuum energy. We discuss the relevance of this mechanism to induce a cosmic bounce, requiring no modified gravity or exotic matter.

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Fluctuations about the Fubini-Lipatov instanton for false vacuum decay in classically scale invariant models

Cited by 13 publications

References 44 publications

Radiative effects on false vacuum decay in Higgs-Yukawa theory

Radiative effects on false vacuum decay in Higgs-Yukawa theory

Functional methods for false-vacuum decay in real time

Double-well instantons in finite volume

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