Vacuum Decay in Theories with Symmetry Breaking by Radiative Corrections

The standard bounce formalism for calculating the decay rate of a metastable vacuum cannot be applied to theories in which the symmetry breaking is due to radiative corrections, because in such theories the tree-level action has no bounce solutions. In this paper I derive a modified formalism to deal with such cases. As in the usual case, the bubble nucleation rate may be written in the form $A e^{-B}$. To leading approximation, $B$ is the bounce action obtained by replacing the tree-level potential by the leading one-loop approximation to the effective potential, in agreement with the generally adopted {\it ad hoc} remedy. The next correction to $B$ (which is proportional to an inverse power of a small coupling) is given in terms of the next-to-leading term in the effective potential and the leading correction to the two-derivative term in the effective action. The corrections beyond these (which may be included in the prefactor) do not have simple expressions in terms of the effective potential and the other functions in the effective action. In particular, the scalar-loop terms which give an imaginary part to the effective potential do not explicitly appear; the corresponding effects are included in a functional determinant which gives a manifestly real result for the nucleation rate.Comment: 39 pages, CU-TP-57

Fate of the false monopoles: induced vacuum decay

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 monopole mass is increased, we find an enhanced rate of decay of the false vacuum relative to the celebrated homogeneous tunneling rate due to Coleman [1].Comment: 10 pages, 4 figure

Flat-top oscillons in an expanding universe

Oscillons are extremely long lived, oscillatory, spatially localized field configurations that arise from generic initial conditions in a large number of non-linear field theories. With an eye towards their cosmological implications, we investigate their properties in an expanding universe. We (1) provide an analytic solution for one dimensional oscillons (for the models under consideration) and discuss their generalization to 3 dimensions, (2) discuss their stability against long wavelength perturbations and (3) estimate the effects of expansion on their shapes and life-times. In particular, we discuss a new, extended class of oscillons with surprisingly flat tops. We show that these flat topped oscillons are more robust against collapse instabilities in (3+1) dimensions than their usual counterparts. Unlike the solutions found in the small amplitude analysis, the width of these configurations is a non-monotonic function of their amplitudes.Comment: v2-matches version published in Phys. Rev D. Updated references and minor modification to section 4.

Benchmarking the Variational Reduced Density Matrix Theory in the Doubly Occupied Configuration Interaction Space with Integrable Pairing Models

The variational reduced density matrix theory has been recently applied with great success to models within the truncated doubly occupied configuration interaction space, which corresponds to the seniority zero subspace. Conservation of the seniority quantum number restricts the Hamiltonians to be based on the SU(2) algebra. Among them there is a whole family of exactly solvable Richardson-Gaudin pairing Hamiltonians. We benchmark the variational theory against two different exactly solvable models, the Richardson-Gaudin-Kitaev and the reduced BCS Hamiltonians. We obtain exact numerical results for the so-called PQGT N-representability conditions in both cases for systems that go from 10 to 100 particles. However, when random single-particle energies as appropriate for small superconducting grains are considered, the exactness is lost but still a high accuracy is obtained.Fil: Rubio García, A.. Instituto de Estructura de la Materia; España. Consejo Superior de Investigaciones Científicas; EspañaFil: Alcoba, Diego Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Capuzzi, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Dukelsky, J.. Consejo Superior de Investigaciones Científicas; España. Instituto de Estructura de la Materia; Españ

Spontaneously Broken Spacetime Symmetries and Goldstone's Theorem

Goldstone's theorem states that there is a massless mode for each broken symmetry generator. It has been known for a long time that the naive generalization of this counting fails to give the correct number of massless modes for spontaneously broken spacetime symmetries. We explain how to get the right count of massless modes in the general case, and discuss examples involving spontaneously broken Poincare and conformal invariance.Comment: 4 pages; 1 figure; v2: minor corrections. version to appear on PR

Numerical Simulation of an Electroweak Oscillon

Numerical simulations of the bosonic sector of the $SU(2)\times U(1)$ electroweak Standard Model in 3+1 dimensions have demonstrated the existence of an oscillon -- an extremely long-lived, localized, oscillatory solution to the equations of motion -- when the Higgs mass is equal to twice the $W^\pm$ boson mass. It contains total energy roughly 30 TeV localized in a region of radius 0.05 fm. A detailed description of these numerical results is presented.Comment: 12 pages, 8 figures, uses RevTeX4; v2: expanded results section, fixed typo

Effective action of a 2+1 dimensional system of nonrelativistic fermions in the presence of a uniform magnetic field: dissipation effects

The effective action of nonrelativistic fermions in 2+1 dimensions is analyzed at finite temperature and chemical potential in the presence of a uniform magnetic field perpendicular to the plane. The method used is a generalization of the derivative expansion technique. The induced Chern-Simons term is computed and shown to exhibit the Hall quantization. Effects of dissipation due to collisions are also analyzed.Comment: 12 page

Probabilistic Approach to Time-Dependent Load-Transfer Models of Fracture

A probabilistic method for solving time-dependent load-transfer models of fracture is developed. It is applicable to any rule of load redistribution, i.e, local, hierarchical, etc. In the new method, the fluctuations are generated during the breaking process (annealed randomness) while in the usual method, the random lifetimes are fixed at the beginning (quenched disorder). Both approaches are equivalent.Comment: 13 pages, 4 figures. To appear in Phys.Rev.

One-Loop Corrections to Bubble Nucleation Rate at Finite Temperature

We present an evaluation of the 1-loop prefactor in the lifetime of a metastable state which decays at finite temperature by bubble nucleation. Such a state is considered in one-component phi^4 model in three space dimensions. The calculation serves as a prototype application of a fast numerical method for evaluating the functional determinants that appear in semiclassical approximations.Comment: DO-TH-93/18, 15 pages, 11 Figures available on request, LaTeX, no macros neede