我们在薄壁极限下（即真真空与假真空近乎简并时）推导了一圈阶的闭式假真空衰变率。我们获得了D维中的bounce位形，以及包含高阶修正、counter-terms和renormalization group running的Euclidean action。我们通过Gel'fand-Yaglom定理提取了低轨道多极与一般轨道多极的函数行列式。低多极出现负本征值与零本征值，并移除了平移零模。我们计算了一般多极的涨落，对轨道模式进行相乘与正规化。我们在D=3,4中求得显式的有限重整化衰变率，并给出任意维度的有限函数行列式闭式表达式。
英文摘要：
We derive a closed-form false vacuum decay rate at one loop in the thin wall limit, where the true and false vacua are nearly degenerate. We obtain the bounce configuration in $D$ dimensions, together with the Euclidean action with a higher order correction, counter-terms and renormalization group running. We extract the functional determinant via the Gel'fand-Yaglom theorem for low and generic orbital multipoles. The negative and zero eigenvalues appear for low multipoles and the translational zeroes are removed. We compute the fluctuations for generic multipoles, multiply and regulate the orbital modes. We find an explicit finite renormalized decay rate in $D = 3, 4$ and give a closed-form expression for the finite functional determinant in any dimension.
We study the decay of "false" domain walls, which are metastable states of the quantum theory where the true vacuum is trapped inside the wall, with the false vacuum outside. We consider a theory with two scalar fields, a shepherd field and a field of sheep. The shepherd field serves to herd the solitons of the sheep field so that they are nicely bunched together. However, quantum tunnelling of the shepherd field releases the sheep to spread out uncontrollably. We show how to calculate the tunnelling amplitude for such a disintegration.
A procedure is reported for numerical analysis of false vacuum transition in a model with multiple scalar fields. It is a refined version of the approach by Konstandin and Huber. The alteration makes it possible to tackle a class of problems that was difficult or unsolvable with the original method, i.e. those with a distant or nonexistent true vacuum. An example with an unbounded-from-below direction is presented.
We find the novel effect on the decay of a false vacuum in view of quantum field theory, which is induced by a field coupling to the scalar field related to a first-order phase transition. This effect of the environment can never be included in the traditional method using the effective potential, and, in fact, acts as dissipative and fluctuation effects on tunneling phenomena. We show that the decay of the false vacuum is drastically either enhanced or suppressed. It is also clarified what kind of interaction enhance or suppress the tunneling probability.
We construct a black hole whose interior is the false vacuum and whose exterior is the true vacuum of a classical field theory. From the outside the metric is the usual Schwarzschild one, but from the inside the space is de Sitter with a cosmological constant determined by the energy of the false vacuum. The parameters of the field potential may allow for the false vacuum to exist for more than the present age of the universe. A potentially relevant effective field theory within the context of QCD results in a Schwarzschild radius of about 200 km.
We consider radiative corrections to false vacuum decay within the framework of quantum mechanics for the general potential of the form 1/2 M q^2 (q-A)(q-B), where M , A and B are arbitrary parameters. For this type of potential we provide analytical results for Green function in the background of corresponding bounce solution together with one loop expression for false vacuum decay rate. Next, we discuss the computation of higher order corrections for false vacuum decay rate and provide numerical expressions for two and three loop contributions.
Recently it was discovered that the Standard Model vacuum may suffer an essential metastability near the Planck scale. In this regard it makes sense to study in more detail the decay processes of the metastable vacuum and to develop methods for their more accurate analysis. In this article we develop a technique to calculate two loop radiative corrections to false vacuum decay rate in thin-wall approximation and apply it to false vacuum decay in scalar quantum field theory with cubic and quartic interactions. The results obtained use dimensional regularization and given in two different renorm…
We study the dynamics of false vacuum bubbles. A nonminimally coupled scalar field gives rise to the effect of negative tension. The mass of a false vacuum bubble from outside observer's point of view can be positive, zero, or negative. The interior false vacuum has de Sitter geometry, while the exterior true vacuum background can have geometry depending on the vacuum energy. We show that there exist expanding false vacuum bubbles without the initial singularity in the past.
I have calculated the exponential suppression factor in the decay rate of the false vacuum (per unit volume) for a real scalar field at finite temperature, in the presence of gravity, in the thin-wall approximation. Temperatures are assumed to be much greater than the inverse of the nucleation radius. The value of a local minimum of the scalar potential is arbitrary. Thus, both true and false vacuua may have arbitrary cosmological constants.
We study the possibility of forming the false vacuum bubble nucleated within the true vacuum background via the true-to-false vacuum phase transition in curved spacetime. We consider a semiclassical Euclidean bubble in the Einstein theory of gravity with a nonminimally coupled scalar field. In this paper we present the numerical computations as well as the approximate analytical computations. We mention the evolution of the false vacuum bubble after nucleation.
The abundance of the QCD axion is known to be suppressed if the Hubble parameter during inflation, $H_{\rm inf}$, is lower than the QCD scale, and if the inflation lasts sufficiently long. We show that the tight upper bound on the inflation scale can be significantly relaxed if the eternal old inflation is driven by the standard-model Higgs field trapped in a false vacuum at large field values. Specifically, $H_{\rm inf}$ can be larger than $100\,$GeV if the false vacuum is located above the intermediate scale. We also discuss the slow-roll inflation after the tunneling from the false vacuum t…
Recent work is reported on inflation model building in the context of supergravity and superstrings, with special emphasis on False Vacuum (`Hybrid') Chaotic Inflation. Globally supersymmetric models do not survive in generic supergravity theories, but fairly simple conditions can be formulated which do ensure successful supergravity inflation. The conditions are met in some of the versions of supergravity that emerge from superstrings.
We study the decay rate of a false vacuum in gauge theory at the one-loop level. We pay particular attention to the case where the bounce consists of an arbitrary number of scalar fields. With a multi-field bounce, which has a curved trajectory in the field space, the mixing among the gauge fields and the scalar fields evolves along the path of the bounce in the field space and the one-loop calculation of the vacuum decay rate becomes complicated. We consider the one-loop contribution to the decay rate with an arbitrary choice of the gauge parameter, and obtain a gauge invariant expression of …
We consider radiative corrections to false vacuum decay in a four-dimensional scalar field theory with cubic and quartic potential. Using planar thin wall approximation we were able to get analytical expression for the decay rate up to two loop order. The results obtained employ dimensional regularization and $\overline{MS}$ renormalization scheme.
We study the dynamics of false vacuum bubbles in the Brans-Dicke theory of gravity by using the thin shell or thin wall approximation. We consider a false vacuum bubble that has a different value for the Brans-Dicke field between the inside false vacuum region and the outside true vacuum region. Within a certain limit of field values, the difference of field values makes the effective tension of the shell negative. This allows new expanding false vacuum bubbles to be seen by the outside observer, which are disallowed in Einstein gravity.
We present a simple and intuitive description of both, the Schwinger effect and false vacuum decay through bubble nucleation, as tunneling problems in one-dimensional relativistic quantum mechanics. Both problems can be described by an effective potential that depends on a single variable of dimension length, which measures the separation of the particles in the Schwinger pair, or the radius of a bubble for the vacuum decay. We show that both problems can be described as tunneling in one-dimensional quantum mechanics if one interprets this variable as the position of a relativistic particle wi…
We consider the Skyrme model modified by the addition of mass terms which explicitly break chiral symmetry and pick out a specific point on the model's target space as the unique true vacuum. However, they also allow the possibility of false vacua, local minima of the potential energy. These false vacuum configurations admit metastable skyrmions, which we call false skyrmions. False skyrmions can decay due to quantum tunnelling, consequently causing the decay of the false vacuum. We compute the rate of decay of the false vacuum due to the existence of false skyrmions.
The decay rate of a false vacuum is studied in gauge theory, paying particular attention to its gauge invariance. Although the decay rate should not depend on the gauge parameter $ξ$ according to the Nielsen identity, the gauge invariance of the result of a perturbative calculation has not been clearly shown. We give a prescription to perform a one-loop calculation of the decay rate, with which a manifestly gauge-invariant expression of the decay rate is obtained. We also discuss the renormalization necessary to make the result finite, and show that the decay rate is independent of the gauge p…
In this work we consider kink-antikink and antikink-kink collisions in a modified $ϕ^4$ model with a false vacuum characterized by a dimensionless parameter $ε$. The usual $ϕ^4$ model is recovered for $ε=0$. We investigate the $ε<<1$ regime where the kink in the presence of false vacuum can be understood as a small deformation of the standard kink for the $ϕ^4$ model. We show that the attractive interaction between the kink-antikink pair leads to a rich scattering pattern, in some cases delaying considerably the false vacuum decay.
In the thin-wall approximation, the decay of a gravitating false vacuum to a lower-energy state is affected by the cosmological horizon structure in both spaces. The nucleation radius of a bubble of true vacuum depends on the surface tension of its boundary and equals the false vacuum cosmological horizon at a critical tension. We argue that there is no tunneling instanton solution beyond the critical tension and argue that there is therefore a bound on allowed membrane tension in theories which rely on semiclassical tunneling to relax the cosmological constant.
We consider a model where a scalar field develops a metastable vacuum state and weakly interacts with another scalar field. In this situation we find the probability of decay of the false vacuum stimulated by the presence and collisions of particles of the second field. The discussed calculation is an illustration of the recently suggested thermal approach to treatment of induced semiclassical processes.
It is shown that there is no chirally symmetric vacuum state in the {cal N}=1 supersymmetric Yang-Mills theory. The values of the gluino condensate and the vacuum energy density are found out through a direct instanton calculation. A qualitative picture of domain wall properties is presented, and a new explanation of the phenomenon of strings ending on the wall is proposed.
This paper reexamines the question of vacuum decay in theories of quantum gravity. In particular it suggests that decay into stable flat or AdS vacua, never occurs. Instead, vacuum decay occurs, if at all, into a cosmological spacetime. If the latter has negative cosmological constant, it undergoes a Big Crunch, which suggests that the whole picture is inconsistent. The question of decay of de Sitter space must be very carefully defined.
We investigate and classify the possible types of false vacuum bubbles in Einstein gravity. The false vacuum bubbles can occur only if gravity is taken into account. We show that there exist solutions only with compact geometries. The analytic computations for the radius and nucleation rate of a vacuum bubble are evaluated using the thin-wall approximation. We discuss possible cosmological implications of our new solutions.
Motivated by cosmological examples we study quantum field theoretical tunnelling from an initial state where the "classical field", i.e. the vacuum expectation value of the field operator is spatially homogeneous but performing a time-dependent oscillation about a local minimum. In particular we estimate both analytically and numerically the exponential contribution to the tunnelling probability. We additionally show that after the tunnelling event, the classical field solution - the so-called "bubble" - mediating the phase transition can either grow or collapse. We present a simple analytical…
The null result in the LHC may indicate that the standard model is not drastically modified up to very high scales such as the GUT/string scale. Having this in the mind, we suggest a novel leptogenesis scenario realized in the false vacuum of the Higgs field. If the Higgs field develops a large vacuum expectation value in the early universe, a lepton number violating process is enhanced, which we use for baryogenesis. To demonstrate the scenario, several models are discussed. For example, we show that the observed baryon asymmetry is successfully generated in the standard model with higher-dim…
We consider the classical static soliton solutions of the Skyrme model with false vacuum potential. We make use of fully three-dimensional relaxation calculations to construct global energy minimizers in the sectors of topological degrees from $Q=1$ to $Q=6$. These solutions may be metastable, they contain a domain of true vacuum inside the core. Further, we explore small regions of negative topological charge density which appear for the Skyrmions of degrees $Q=3,5,6$.
In this presentation, we discuss the nucleation and subsequent evolution of false vacuum bubbles in the scalar-tensor gravity. First, we transform the scalar-tensor type theory of gravity to the standard Brans-Dicke type. Second, we transform the Brans-Dicke type theory from the Jordan frame to the Einstein frame. For a certain potential, a true vacuum bubble in the Einstein frame can be transformed to a false vacuum bubble in the Jordan frame by a conformal transformation. Thus, in the Jordan frame, the nucleation of a false vacuum bubble can be possible and its subsequent evolution can be de…
In this work we show a class of oscillating configurations for the evolution of the domain walls in Euclidean space. The solutions are obtained analytically. Phase transitions are achieved from the associated fluctuation determinant, by the decay rates of the false vacuum.
Motivated by the work of Mersini, the particle production related to the tunneling in false vacuum decay is carefully investigated in the thin-wall approximation. It is shown that in this case the particle production is exponentially suppressed even when the momentum is comparable to the curvature scale of the bubble. The number of created particles is ultraviolet finite.
We calculate the three-point correlation function of the comoving curvature perturbation generated during an inflationary epoch driven by false vacuum energy. We get a novel false vacuum shape bispectrum, which peaks in the equilateral limit. Using this result, we propose a scenario which we call "old curvaton". The shape of the resulting bispectrum lies between the local and the false vacuum shapes. In addition we have a large running of the spectral index.
With the Higgs mass now measured at the sub-percent level, the potential metastability of the electroweak vacuum of the Standard Model (SM) motivates renewed study of false vacuum decay in quantum field theory. In this note, we describe an approach to calculating quantum corrections to the decay rate of false vacua that is able to account fully and self-consistently for the underlying inhomogeneity of the solitonic tunneling configuration. We show that this method can be applied both to theories in which the instability arises already at the level of the classical potential and those in which …
We study a gauge theory model where there is an intermediate symmetry breaking to a meta- stable vacuum that breaks a simple gauge group to a U (1) factor. Such models admit the existence of meta-stable magnetic monopoles, which we dub false monopoles. We prove the existence of these monopoles in the thin wall approximation. We determine the instantons for the collective coordinate that corresponds to the radius of the monopole wall and we calculate the semi-classical tunneling rate for the decay of these monopoles. The monopole decay consequently triggers the decay of the false vacuum. As the…
We investigate dielectric branes in false vacua in Type IIB string theory. The dielectric branes are supported against collapsing by lower energy vacua inside spherical or tube-like branes. We claim that such branes can be seeds for semi-classical (or quantum mechanical) decay of the false vacua, which makes the life-time of the false vacua shorter. Also, we discuss a topology change of a bubble corresponding to the fuzzy monopole triggered by dissolving fundamental strings.
We discuss an exact false vacuum decay rate at one loop for a real and complex scalar field in a quartic-quartic potential with two tree-level minima. The bounce solution is used to compute the functional determinant from both fluctuations. We obtain the finite product of eigenvalues and remove translational zero modes. The orbital modes are regularized with the zeta function and we end up with a complete renormalized decay rate. We derive simple expansions in the thin and thick wall limits and determine their validity.
We describe here how the late time behavior of the decaying states, which is predicted to deviate from an exponential form, while normally of insignificant consequence, may have important cosmological implications in the case of false vacuum decay. It may increase the likelihood of eternal inflation, and may help explain the likelihood of observing a small vacuum energy at late times, as well as arguing against decay into a large negative energy (anti-de Sitter space), vacuum state as has been motivated by some string theory considerations. Several interesting open questions are raised, includ…
We study a false vacuum decay in a two-dimensional black hole spacetime background. The decay rate in the case that nucleation site locates at a black hole center has been calculated in the literature. We develop a method for calculating the decay rate of the false vacuum for a generic nucleation site. We find that the decay rate becomes larger when the nucleation site is close to the black hole horizon and coincides with that in Minkowski spacetime when the nucleation site goes to infinity.
A model that gives rise to vacuum bubbles is considered where the domain wall field interacts with another real scalar field, resulting in the formation of domain ribbons within the host domain wall. Ribbon-antiribbon annihilations produce elementary bosons whose mass inside the wall is different from the mass in vacuum. Two cases are considered, where the bosons get trapped either within the bubble wall or the bosons get trapped within the vacuum enclosed by the bubble. The bosonic (meta)stabilization effect on the bubble is examined in each case. It is found that when the bosons become trapp…
We study false vacuum decay catalyzed by black holes. We consider a toy two-dimensional model of a scalar field with an unstable potential in the background of a dilaton black hole. A realistic black hole in four dimensions possesses the potential barrier for linear field perturbations. We model this barrier -- the greybody factor -- for spherically-symmetric perturbations in the toy model by adding a coupling between the scalar field and dilaton. We compute analytically the decay rate for the black hole in thermal equilibrium (Hartle-Hawking state) and for the radiating black hole in empty sp…
We analyze properties of unstable vacuum states from the point of view of the quantum theory. In the literature one can find some suggestions that some of false (unstable) vacuum states may survive up to times when their survival probability has a non-exponential form. At asymptotically late times the survival probability as a function of time $t$ has an inverse power--like form. We show that at this time region the energy of the false vacuum states tends to the energy of the true vacuum state as $1/t^{2}$ for $t \to \infty$. This means that the energy density in the unstable vacuum state shou…
False vacuum decay around black holes: calculation from first principles in the (3+1)-dimensional case
Institute for Nuclear Research of the Russian Academy of Sciences（俄罗斯科学院核物理研究所）；Physics Faculty, Lomonosov Moscow State University（莫斯科国立大学物理系）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Institute for Theoretical and Mathematical Physics, MSU（莫斯科国立大学理论与数学物理研究所）
An effective one-loop action built from the soliton field itself for the two-dimensional (2D) problem of soliton pair creation is proposed. The action consists of the usual mass term and a kinetic term in which the simple derivative of the soliton field is replaced by a covariant derivative. In this effective action the soliton charge is treated no longer as a topological charge but as a Noether charge. Using this effective one-loop action, the soliton-antisoliton pair production rate is calculated and one recovers Stone's exponential factor and the prefactor of Kiselev, Selivanov and Voloshin…
In the present paper we develop the self-consistent $Spin(4,4)$-invariant model of the unification of gravity with weak $SU(2)$ interactions in the assumption of the existence of visible and invisible sectors of the Universe. It was shown that the consequences of the multiple point principle predicting two degenerate vacua in the Standard Model (SM) suggest a theory of Inflation, in which the inflaton field $σ$ starts trapped in a cold coherent state in the "false vacuum" of the Universe at the value of the Higgs field's VEV $v\sim 10^{18}$ GeV (in the visible world). Then the inflations of th…
We present a general numerical method for computing precisely the false vacuum decay rate, including the prefactor due to quantum fluctuations about the classical bounce solution, in a self-interacting scalar field theory modeling the process of nucleation in four dimensional spacetime. This technique does not rely on the thin-wall approximation. The method is based on the Gelfand-Yaglom approach to determinants of differential operators, suitably extended to higher dimensions using angular momentum cutoff regularization. A related approach has been discussed recently by Baacke and Lavrelashvi…
We introduce a Green's function method for handling radiative effects on false vacuum decay. In addition to the usual thin-wall approximation, we achieve further simplification by treating the bubble wall in the planar limit. As an application, we take the $λϕ^4$ theory, extended with $N$ additional heavier scalars, wherein we calculate analytically both the functional determinant of the quadratic fluctuations about the classical soliton configuration and the first correction to the soliton configuration itself.
We study the stability of supersymmetry breaking vacuum in the presence of cosmic strings arising in the messenger sector. For certain ranges of the couplings, the desired supersymmetry breaking vacua become unstable against decay into phenomenologically unacceptable vacua. This sets constraints on the range of allowed values of the coupling constants appearing in the models and more generally on the chosen dynamics of gauge symmetry breaking.
We study negative modes around the Coleman-de Luccia bounce solution. The conditions for the appearance of an infinite number of the negative modes do not coincide between Lagrangian and Hamiltonian formulations in the literature, and we discuss the origin of this difference in detail. We show how different choices of the variable for the fluctuation around the bounce solution affect the negative mode condition in the Hamiltonian approach, and point out that there exists a choice which gives the same negative mode condition as the Lagrangian approach.
We review the description of tunnelling phenomena in the semi-classical approximation in ordinary quantum mechanics and in quantum field theory. In particular, we describe in detail the calculation, up to the first quantum corrections, of the decay probability per unit time of a metastable ground state. We apply the relevant formalism to the case of the standard model of electroweak interactions, whose ground state is metastable for sufficiently large values of the top quark mass. Finally, we discuss the impact of gravitational interactions on the calculation of the tunnelling rate.
This paper studies false vacuum lumps surrounded by the true vacuum in a real scalar field potential in flat spacetime. Fermions reside in the core of the lump, which are coupled with the scalar field via Yukawa interaction. Such lumps are stable against spherical collapse and deformation from spherical shape based on energetics considerations. The fermions inside the lump are treated as a uniform Fermi gas. We consider the Fermi gas in both ultrarelativistic and nonrelativistic limits. The mass and size of these lumps depend on the scale characterizing the scalar field potential as well as th…
We consider the noncommutative Abelian-Higgs theory and construct new types of exact multi-vortex solutions that solve the static equations of motion. They in general do not follow from the BPS equations; only for some specific values of parameters, they satisfy the BPS equations saturating the Bogomol'nyi bound. We further consider the Abelian-Higgs theory with more complicated scalar potential allowing unstable minima and construct exact solutions of noncommutative false vacuum bubble with integer magnetic flux. The classical stability of the solutions is discussed.
