Euclidean Bounce Research Articles

Thin-wall vacuum decay in the presence of a compact dimension

We study the problem of false vacuum decay in arbitrary dimensions, in the presence of gravity, and compute the transition probability within the thin-wall approximation, generalising the results of Coleman and de Luccia. In the particular case of one compact dimension, we present explicit formulae for the Euclidean Bounce configuration that drives the transition from a de Sitter to Minkowski or from a Minkowski to anti-de Sitter vacua.

Quartic Gradient Flow

Saddle-point configurations, such as the Euclidean bounce and sphalerons, are known to be difficult to find numerically. In this letter we study a new method, Quartic Gradient Flow, to search for such configurations. The central idea is to introduce a gradient-flow-like equation in such a way that all the fluctuations around the saddle-point have eigenvalues that are square of the eigenvalues of the original quadratic operator. We illustrate how the method works for the Euclidean bounce and sphalerons.

Tunneling potential actions from canonical transformations

A new formulation for obtaining the tunneling action for vacuum decay based on the so-called tunneling potential was developed recently. In the original derivation, the new actionwas obtained by requiring that its variation led to the correct equations of motion and the same value for the action as evaluated on the Euclidean bounce. We present an alternative derivation of the tunneling potential action via canonical transformations. We discuss both single-field and multi-field cases as well as the case with gravity. We also comment on the possible application of the new approach to the calculation of the functional determinant prefactor in the tunneling rate.

Vacuum decay actions from tunneling potentials for general spacetime dimension

The tunneling potential method to calculate the action for vacuum decay is an alternative to the Euclidean bounce method that has a number of attractive features. In this paper we extend the formalism to general spacetime dimension d > 2 and use it to give simple proofs of several results. For Minkowski or Anti de Sitter false vacua, we show that gravity or higher barriers increase vacuum lifetime and describe a very clean picture of gravitational quenching of vacuum decay. We also derive the thin-wall limit of the action, show how detailed balance for dS to dS transitions works in the new formalism and how to obtain potentials for which the vacuum decay solution can be obtained analytically.

FindBounce: Package for multi-field bounce actions

We are launching FindBounce, a Mathematica package for the evaluation of the Euclidean bounce action that enters the decay rate of metastable states in quantum and thermal field theories. It is based on the idea of polygonal bounces, which is a semi-analytical approach to solving the bounce equation by discretizing the potential into piecewise linear segments. This allows for a fast and robust evaluation of arbitrary potentials with specified precision and any number of scalar fields. Time cost grows linearly with the number of fields and/or the number of segments. Computation with 20 fields takes ∼2 s with 0.5% accuracy of the action. The FindBounce function is simple to use with the native Mathematica look and feel, it is easy to install, and comes with detailed documentation and physical examples, such as the calculation of the nucleation temperature. We also provide timing benchmarks with comparisons to existing tools, where applicable. Program summaryProgram title:FindBounceCPC Library link to program files:http://dx.doi.org/10.17632/tysw84skx3.1Developer’s repository link:https://github.com/vguada/FindBounceLicensing provisions: GNU General Public License 3Programming language:MathematicaNature of problem: Evaluation of the Euclidean bounce action that controls the decay rate of metastable local minima in thermal and quantum field theories.Solution method: Semi-analytical solution of a system of coupled differential equations, based on the polygonal bounce idea (Guada et al., 2019).Restrictions:Mathematica version 10 or above, works in D=3,4.

Angular momentum and gravimagnetization of the N=2 supersymmetric vacuum

In this note we discuss the gravimagnetization of the ${\cal N}=2$ SYM vacuum in the $\Omega$-background. It is argued that the Seiberg-Witten prepotential is related to the vacuum density of the angular momentum in the Euclidean $R^4$ space. The possible role of the dyonic instantons as the microscopic angular momentum carriers which could yield the spontaneous vacuum gravimagnetization is conjectured. We interpret the dyonic instanton as a kind of the Euclidean bounce in $R^4$ similar to one responsible for the Schwinger pair creation. The induced angular momentum in $R^4$ is also briefly considered in the dual Liouville formulation of $SU(2)$ theory via AGT relation.

M-branes and metastable states

We study a supersymmetry breaking deformation of the M-theory background found in arXiv:hep-th/0012011. The supersymmetric solution is a warped product of R^{2,1} and the 8-dimensional Stenzel space, which is a higher dimensional generalization of the deformed conifold. At the bottom of the warped throat there is a 4-sphere threaded by \tilde{M} units of 4-form flux. The dual (2+1)-dimensional theory has a discrete spectrum of bound states. We add p anti-M2 branes at a point on the 4-sphere, and show that they blow up into an M5-brane wrapping a 3-sphere at a fixed azimuthal angle on the 4-sphere. This supersymmetry breaking state turns out to be metastable for p / \tilde{M} < 0.054. We find a smooth O(3)-symmetric Euclidean bounce solution in the M5-brane world volume theory that describes the decay of the false vacuum. Calculation of the Euclidean action shows that the metastable state is extremely long-lived. We also describe the corresponding metastable states and their decay in the type IIA background obtained by reduction along one of the spatial directions of R^{2,1}.

Dynamical Decay of Brane-Antibrane and Dielectric Brane

Using D-brane effective field theories, we study dynamical decay of unstable brane systems : (i) a parallel brane-antibrane pair with separation l and (ii) a dielectric brane. In particular we give explicitly the decay width of these unstable systems, and describe how the decay proceeds after the tunnel effect. The decay (i) is analysed by the use of a tachyon effective action on the Dp-Dpbar. A pair annihilation starts by nucleation of a bubble of a tachyon domain wall which represents a throat connecting these branes, and the tunneling decay width is found to be proportional to exp(-l^{p+1} T_{Dp}). We study also the decay leaving topological defects corresponding to lower-dimensional branes, which may be relevant for recent inflationary braneworld scenario. As for the decay (ii), first we observe that Dp-branes generically ``curl up'' in a nontrivial RR field strength. Using this viewpoint, we compute the decay width of the dielectric D2-branes by constructing relevant Euclidean bounce solutions in the shape of a funnel. We also give new solutions in doughnut shape which are involved with nucleation of dielectric branes from nothing.

False vacuum decay with gravity in the non-thin-wall limit

We consider a wave-function approach to the false vacuum decay with gravity and present a new method to calculate the tunneling amplitude under the WKB approximation. The result agrees with the one obtained by the Euclidean path-integral method, but gives a much clearer interpretation of an instanton (Euclidean bounce solution) that dominates the path integral. In particular, our method is fully capable of dealing with the case of a thick wall with the radius of the bubble comparable to the radius of the instanton, thus surpassing the path-integral method whose use can be justified only in the thin-wall and small bubble radius limit. The calculation is done by matching two WKB wave functions, one with the final state and another with the initial state, with the wave function in the region where the scale factor of the metric is sufficiently small compared with the inverse of the typical energy scale of the field potential at the tunneling. The relation of the boundary condition on our wave function for the false vacuum decay with the Hartle-Hawking no-boundary boundary condition and Vilenkin's tunneling boundary condition on the wave function of the universe is also discussed.

Gauged monopole-bubble

The decay of a metastable false vacuum by bubble nucleation is studied in the high temperature limit of the gauge theory in which an SO(3) gauge symmetry is spontaneously broken to an SO(2). The effects of internal symmetry are so drastic that, in addition to the known Euclidean bounce solution, there exists a new bubble solution involving a 't Hooft–Polyakov monopole at its center the moment it is nucleated. The decay rate and evolution are analyzed.

No supercritical supercurvature mode conjecture in one-bubble open inflation

In the path integral approach to false vacuum decay with the effect of gravity, there is an unsolved problem, called the negative mode problem. We show that the appearance of a supercritical supercurvature mode in the one-bubble open inflation scenario is equivalent to the existence of a negative mode around the Euclidean bounce solution. Supercritical supercurvature modes are those whose mode functions diverge exponentially for large spatial radius on the time constant hypersurface of the open universe. Then we propose a conjecture that there should be ``no supercritical supercurvature mode''. For a class of models that contains a wide variety of tunneling potentials, this conjecture is shown to be correct.

False vacuum decay with gravity: Negative mode problem

Motivated by work of Lavrelashvili, Rubakov and Tinyakov (LRT), who claim that the WKB approximation would break down even at energy scale far below the Planck one, the decay of false vacuum under the presence of gravity is carefully investigated. First we approach the issue from a different point of view, namely, by solving the Wheeler-DeWitt equation under the boundary condition appropriate for the false vacuum decay. The resulting wave function shows no sign of the break-down of the WKB approximation. Then, based on the canonical Hamiltonian form of the Euclidean path integral, we develop a method to analyze the number of negative modes around the Euclidean bounce solution describing the tunneling process and evaluate it in some limiting cases. Again, we find a strong evidence that LRT's claim is superficial.

False Vacuum Decay with Gravity: Negative Mode Problem

Motivated by work of Lavrelashvili, Rubakov and Tinyakov (LRT), who claim that the WKB approximation would break down even at energy scale far below the Planck one, the decay of false vacuum under the presence of gravity is carefully investigated. First we approach the issue from a different point of view, namely, by solving the Wheeler-DeWitt equation under the boundary condition appropriate for the false vacuum decay. The resulting wave function shows no sign of the break-down of the WKB approximation. Then, based on the canonical Hamiltonian form of the Euclidean path integral, we develop a method to analyze the number of negative modes around the Euclidean bounce solution describing the tunneling process and evaluate it in some limiting cases. Again, we find a strong evidence that LRT's claim is superficial.

Quantum nucleation of false-vacuum bubbles.

We show that a small bubble of false vacuum can tunnel to the critical size for inflation, and calculate the amplitude in leading WKB approximation. An initially nonsingular space becomes and exterior space plus a baby universe (which contains the bubble), joined by a black-hole singularity. We work in a Hamiltonian formalism; the corresponding Euclidean bounce is shown to have a degenerate vierbein.

Wormholes with a past

We discuss Minkowski space interpretations of euclidean solutions which provide semiclassical approximations to quantum processes. In particular, we consider wormhole and euclidean bounce solutions. We argue that the semiclassical description involves an instantaneous discontinuity in the Minkowski signature classical evolution and that the euclidean solutions provide final and initial value data on either side of this discontinuity. In the case of the de Sitter wormhole and bounce solutions, we resolve the problem of having a single maximal surface on the euclidean solution which must provide both past and future data across the Minkowski signature discontinuity.