Out of Equilibrium Dynamics of Supersymmetry at High Energy Density

We investigate the out of equilibrium dynamics of global chiral supersymmetry at finite energy density. We concentrate on two specific models. The first is the massive Wess-Zumino model which we study in a selfconsistent one-loop approximation. We find that for energy densities above a certain threshold, the fields are driven dynamically to a point in field space at which the fermionic component of the superfield is massless. The state, however is found to be unstable, indicating a breakdown of the one-loop approximation. To investigate further, we consider an O(N) massive chiral model which is solved exactly in the large $N$ limit. For sufficiently high energy densities, we find that for late times the fields reach a nonperturbative minimum of the effective potential degenerate with the perturbative minimum. This minimum is a true attractor for O(N) invariant states at high energy densities, and this provides a mechanism for determining which of the otherwise degenerate vacua is chosen by the dynamics. The final state for large energy density is a cloud of massless particles (both bosons and fermions) around this new nonperturbative supersymmetric minimum. By introducing boson masses which softly break the supersymmetry, we demonstrate a see-saw mechanism for generating small fermion masses. We discuss some of the cosmological implications of our results.Comment: 31 pages, 15 figure

Nonequilibrium dynamics in scalar hybrid models

We study by numerical simulations the transition from the metastable "false vacuum" to the broken symmetry phase in the preheating stage after cosmic inflation in a scalar hybrid model. We take quantum fluctuations and their back reaction into account by applying a one-loop bubble-resummation.Comment: 5 pages, 4 figures, contribution to the conference Strong and Electroweak Matter (SEWM2004), Helsinki, Finland, 16-19 June 200

Nonequilibrium evolution and symmetry structure of the large-N Φ4\Phi^4 model at finite temperature

We consider the large-N $\Phi^4$ theory with spontaneously broken symmetry at finite temperature. We study, in the large-N limit, quantum states which are characterized by a time dependent, spatially homogenous expectation value of one of the field components, $\phi_N(t)$, and by quantum fluctuations of the other $N-1$ components, that evolve in the background of the classical field. Investigating such systems out of equilibrium has recently been shown to display several interesting features. We extend here this type of investigations to finite temperature systems. Essentially the novel features observed at T=0 carry over to finite temperature. This is not unexpected, as the main mechanisms that determine the late-time behavior remain the same. We extend two empirical - presumably exact - relations for the late-time behavior to finite temperature and use them to define the boundaries between the region of different asymptotic regimes. This results in a phase diagram with the temperature and the initial value of the classical field as parameters, the phases being characterized by spontaneous symmetry breaking resp. symmetry restoration. The time evolution is computed numerically and agrees very well with the expectations.Comment: 21 pages, 13 Figures, LaTeX, some typos correcte

Scalar O(N) Model at Finite Temperature -- 2PI Effective Potential in Different Approximations

We calculate the two-particle irreducible (2PI) effective potential of the O(N) linear sigma model in 1+1 dimensions. The approximations we use are the next-to-leading order of a 1/N expansion (for arbitrary N) and a kind of "resummed loop approximation" for N=1. We show that the effective potential of the 1/N expansion is convex for N=4 and N=10 whereas it is not for the "loop" expansion and the case N=1 of the 1/N expansion.Comment: LaTeX, 5 pages. Contribution to the Proceedings of 6th Conference on Strong and Electroweak Matter 2004 (SEWM04), Helsinki, Finland, 16-19 Jun 200

One-loop corrections to the Nielsen-Olesen vortex: collective oscillations

We connect the translation modes of the instanton in the two-dimensional Abelian Higgs model with local translations of the vortex of the related model in (3+1) dimensions, the Nielsen-Olesen vortex. In this context these modes describe collective oscillations of the string. We construct the wave function of this mode and we derive, via a virial theorem, an effective action for these oscillations, which is consistent with the action constructed by Nielsen and Olesen using general arguments. We discuss some aspects of renormalization, based on a recent computation of one loop corrections to string tension of the vortex.Comment: 18 pages, 1 figur

One-loop corrections to the metastable vacuum decay

We evaluate the one-loop prefactor in the false vacuum decay rate in a theory of a self interacting scalar field in 3+1 dimensions. We use a numerical method, established some time ago, which is based on a well-known theorem on functional determinants. The proper handling of zero modes and of renormalization is discussed. The numerical results in particular show that quantum corrections become smaller away from the thin-wall case. In the thin-wall limit the numerical results are found to join into those obtained by a gradient expansion.Comment: 31 pages, 7 figure

Self-consistent bounces in two dimensions

We compute bounce solutions describing false vacuum decay in a Phi**4 model in two dimensions in the Hartree approximation, thus going beyond the usual one-loop corrections to the decay rate. We use zero energy mode functions of the fluctuation operator for the numerical computation of the functional determinant and the Green's function. We thus avoid the necessity of discretizing the spectrum, as it is necessary when one uses numerical techniques based on eigenfunctions. Regularization is performed in analogy of standard perturbation theory; the renormalization of the Hartree approximation is based on the two-particle point-irreducible (2PPI) scheme. The iteration towards the self-consistent solution is found to converge for some range of the parameters. Within this range we find the corrections to the leading one-loop approximation to be relatively small, not exceeding one order of magnitude in the total transition rate.Comment: 30 pages, 12 figure

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Translation of the German original

Nonequilibrium dynamics: a renormalized computation scheme

We present a regularized and renormalized version of the one-loop nonlinear relaxation equations that determine the non-equilibrium time evolution of a classical (constant) field coupled to its quantum fluctuations. We obtain a computational method in which the evaluation of divergent fluctuation integrals and the evaluation of the exact finite parts are cleanly separated so as to allow for a wide freedom in the choice of regularization and renormalization schemes. We use dimensional regularization here. Within the same formalism we analyze also the regularization and renormalization of the energy-momentum tensor. The energy density serves to monitor the reliability of our numerical computation. The method is applied to the simple case of a scalar phi^4 theory; the results are similar to the ones found previously by other groups.Comment: 15 pages, 9 postscript figures, revtex; version published in Phys. Rev, with minor corrections; improves the first version of 1996 by including the discussion of energy momentum tenso