False Vacuum Decay with Gravity in a Critical Case

The vacuum decay in a de Sitter universe is studied for the class of effective inflaton potentials that curvature at the top is less than as well as greater than a critical value determined previously. By comparing the actions of the Hawking - Moss instanton and the Coleman - de Luccia instanton(s) the mode of vacuum decay is determined in this critical situation.     

Gauss–Bonnet term on vacuum decay

We study the effect of the Gauss–Bonnet term on vacuum decay process in the Coleman–De Luccia formalism. The Gauss–Bonnet term has an exponential coupling with the real scalar field, which appears in the low energy effective action of string theories. We calculate numerically the instanton solution, which describes the process of vacuum decay, and obtain the critical size of bubble. We find that the Gauss–Bonnet term has a nontrivial effect on the false vacuum decay, depending on the Gauss–Bonnet coefficient.     

Does string theory predict an open universe?

It has been claimed that the string landscape predicts an open universe, with negative curvature. The prediction is a consequence of a large number of metastable string vacua, and the properties of the Coleman–De Luccia instanton which describes vacuum tunneling. We examine the robustness of this claim, which is of particular importance since it seems to be one of string theory's few claims to falsifiability. We find that, due to subleading tunneling processes, the prediction is sensitive to unknown properties of the landscape. Under plausible assumptions, universes like ours are as likely to be closed as open.     

Coleman–de Luccia Instanton of the Second Order in a Brane World

The second order Coleman–de Luccia instanton and its action in the Randall–Sundrum type II model are investigated and the comparison with the results in Einstein’s general relativity is done in the present paper. PACS Numbers: 98.80.Cq.     

Spectrum of heavy quarkonia in an instanton medium

The energy-level shift in heavy-quarkonium systems that is caused by fluctuations of vacuum gluon fields is estimated by simulating these fields by an instanton liquid. The use of the corresponding vacuum correlation function makes it possible to go beyond the dipole approximation. The width of energy levels with respect to decay to e ⁺ e ^? pairs is also given. It is shown that, both for bottomonium and for charmonium systems, an instanton medium can ensure a scale of shifts and widths of levels that is compatible with experimental data. In particular, it is indicated that a sizable logarithmic contribution at short distances is peculiar to the instanton vacuum.     

Properties of Charmonium States in a Phenomenological Approach

We investigate the spectrum and decay rates of charmonium states within the framework of the non relativistic quark model by employing a Coulomb like potential from the perturbative one gluon exchange and the linear confining potential along with the potential derived from instanton vacuum to account for the hyperfine mass splitting of charmonium states in variational approach. We predict radiative E1, M1, two-photon, lepton and two-gluon decay rates of low lying charmonium states. An overall agreement is obtained with the experimental masses and decay widths.We have estimated the branching ratio of two gluons decaying into light hadrons.     

PATH INTEGRAL CALCULATION OF QUANTUM TUNNELING FOR CUBIC POTENTIAL AT FINITE TEMPERATURE

The periodic instanton method is used to study the decay rates of metastable ground state and excited states of the cubic potential. The imaginary part of the energy is calculated through the standard procedure in the path-integral scheme. A formula of the decay rate valid for the entire region of energy is obtained. This formula provides a linkage between classical thermal activation at high temperatures and purely quantum tunneling at zero temperature. It is shown that in the low energy limit this more general result reduces exactly to the vacuum result. The temperature dependence of the decay rate agrees with earlier works in the literature.     

Gluon field strength correlation functions within a constrained instanton model

We suggest a constrained instanton (CI) solution in the physical QCD vacuum which is described by large-scale vacuum field fluctuations. This solution decays exponentially at large distances. It is stable only if the interaction of the instanton with the background vacuum field is small and additional constraints are introduced. The CI solution is explicitly constructed in the ansatz form, and the two-point vacuum correlator of the gluon field strengths is calculated in the framework of the effective instanton vacuum model. At small distances the results are qualitatively similar to the single instanton case; in particular, the invariant structure is small, which is in agreement with the lattice calculations. Received: 18 June 1999 / Revised version: 21 July 1999 / Published online: 17 February 2000     

Vacuum decay and the effective action at finite temperature

The problem of vacuum decay at finite temperature is discussed. It is shown that, when the unstable minimum in the potential arises via quantum effects, the corrections to the kinetic terms cannot be ignored since they are singular. This means that previous adaptations of the instanton method to realistic models are suspect. We also discuss alternative methods of calculations which may be able to avoid the problem.     

Conformally coupled scalars, instantons, and vacuum instability in 4D anti-de Sitter space

We show that a scalar field conformally coupled to AdS gravity in four dimensions with a quartic self-interaction can be embedded into M theory. The holographic effective potential is exactly calculated, allowing us to study nonperturbatively the stability of AdS4 in the presence of the conformally coupled scalar. It is shown that there exists a one-parameter family of conformal scalar boundary conditions for which the boundary theory has an unstable vacuum. In this case, the bulk theory has instanton solutions that mediate the decay of the AdS4 space. These results match nicely with the vacuum structure and the existence of instantons in an effective three-dimensional boundary model.     

Calorons and the bilocal correlator of the gluon-field strength

The bilocal correlator for finite-temperature gluodynamics is calculated in the instanton gas model. It is shown that the correlation length of vacuum in this model decreases when temperature increases. The results are compared with finite-temperature lattice calculations for the bilocal correlator. The instanton density and possible structures of nonperturbative vacuum are discussed.     

Heavy quarkonia properties at high temperatures

The spectra and e ⁺ e ⁻ decay widths of the heavy quarkonia as a function of the temperature of medium generated in the ultrarelativistic heavy-ion collisions are discussed. The fluctuations of the vacuum gluon fields are estimated within the instanton liquid model approach. It is noticed that the parameters that are considered can be used to indicate the gluon warming.     

On the possibility of the dual Meissner effect induced by instantons

The classical Yang-Mills equation of motion is numerically investigated in the Lorentz gauge for a SU(2) gauge group. The color-electric field of two point-like charges is studied in the “empty” vacuum and in a state with an instanton present. The major effect for a fixed orientation of the instanton is that the color-electric field lines are expelled or attracted from the instanton region depending on the orientation of the instanton. If over the orientations of the instanton is averaged, this effect drops out. In this case of a random instanton orientation, we find that the external color-electric field is expelled from the instanton core. The origin of this effect is discussed. Received: 5 September 1997 / Published online: 23 February 1998     

Spin effects in instanton models

Nonperturbative nolocal structure of QCD vacuum is well described by instanton model. Specific helicity and flavor structure of zero modes of quarks, in instanton field allows simultaneously to explain some important features of low-and high-energy hadron phenomemology. The basic characteristics of hadron spectrum, partonic sum rules, heavyquark potential etc within the instanton liquid model are briefly discussed.     

Information on the QCD phase transition and the vacuum permeability from the interquark potential

A method for the calculation of the interquark potential resulting from the instanton induced phase transition in the QCD vacuum is described and it is shown that good agreement is obtained with successful phenomenological potentials for parameter values close to those expected from naive instanton calculations.     

A general scheme for computation of instanton effects

A general approach to the computation of instanton effects without invoking an ad hoc cut-off on their size is illustrated here by the computation of instanton contributions to the static $\text{Q}$Q potential and vacuum polarization. Our results suggest that the instanton effects are much smaller than perturbative effects in the region where both may be reliably computed.     

Quantum codimension-two cosmology

We generalize the 2-codimensional quantum cosmological model with the vacuum seed instanton to that with a non-vacuum seed instanton associated with the Gibbons–Townsend monopole. The confusion in the literature that substituting a field configuration into an action and varying that action is not equivalent to substituting it into the field equations is clarified.     

Properties of lightest mesons at finite temperature and quark/baryon chemical potential in the instanton model of the QCD vacuum

The paper is focused on calculating the finite temperature and quark/baryon chemical potential dependencies of the quark condensate and the π-and σ-meson masses in the subcritical region in the instanton model of the QCD vacuum. The impact of phononlike excitation of instanton liquid on the characteristics of the σ meson in such an environment is also examined.     

Off-diagonal quark distributions in pions in the effective single-instanton approximation

Nonperturbative functions that parametrize off-diagonal hadronic matrix elements of the light-cone leading-twist quark operators are considered. These functions are calculated within the proposed relativistic quark model allowing for the nontrivial structure of the QCD vacuum, special attention being given to gauge invariance. Hadrons are treated as bound states of quarks; strong-interaction quark-pion vertices are described by effective interaction Lagrangians generated by instantons. The parameters of the instanton vacuum, such as the effective radius of the instanton and the quark mass, are related to the vacuum expectation values of the quark-gluon operators of the lowest dimension and to low-energy pion observables.