A confederacy of anomalies
A personal recollection of early years in lattice gauge theory with a bias towards chiral symmetry and lattice fermions.
hep-lat↗
arXiv subjects
Jan Smit
Publications and source records attributed to Jan Smit.
Co\"{o}rdinate transformations, metrics and black hole features in the collapsed phase of EDT
This is a companion article to `Using massless fields for observing black hole features in the collapsed phase of Euclidean dynamical triangulations' [1]. It clarifies a singular co\"{o}rdinate transformation of an $SO(4)$ invariant metric to the usual spherical co\"{o}rdinates in which, at an instant of time called zero, the metric takes the form of a black hole with an interior. Regular transformations are also studied and found to lead in the zero time limit to the same spatial components of the metric as with the singular one, whereas the time component ends up differently. Components of the Einstein tensor also end up the same. A regular black hole metric is inversely transformed and compared with simulation results in [1].
gr-qc↗
Using massless fields for observing black hole features in the collapsed phase of Euclidean dynamical triangulations
We report on an old computation of propagators of massless scalar fields on an ensemble of configurations in 4D Euclidean dynamical triangulations in the collapsed (crumpled) phase. The resulting quantum average is used to construct the scale factor of a 4-D rotational invariant metric. This new scale factor is non-zero at the origin, which we assume to be caused the presence of the well-known singular structure in the collapsed phase. The scale factor depends on an overall integration constant, which is determined by comparison with the implied volume at intermediate distances. We construct a transformation to a 3-D rotational invariant metric, which reveals Euclidean black hole features at an instant in time, with a horizon separating interior and exterior parts. Effective Einstein equations in the presence of a `geometric condensate' are assumed, and computed with the software OGRe. Also explored briefly is a qualitatively different (not preferred) interpretation of the data which follows from comparison with an inversely transformed Euclidean regular black hole metric.
gr-qc↗
Three models of non-perturbative quantum-gravitational binding
Known quantum and classical perturbative long-distance corrections to the Newton potential are extended into the short-distance regime using evolution equations for a `running' gravitational coupling, which is used to construct examples non-perturbative potentials for the gravitational binding of two particles. Model-I is based on the complete set of the relevant Feynman diagrams. Its potential has a singularity at a distance below which it becomes complex and the system gets black hole-like features. Model-II is based on a reduced set of diagrams and its coupling approaches a non-Gaussian fixed point as the distance is reduced. Energies and eigenfunctions are obtained and used in a study of time-dependent collapse (model-I) and bouncing (both models) of a spherical wave packet. The motivation for such non-perturbative `toy' models stems from a desire to elucidate the mass dependence of binding energies found 25 years ago in an explorative numerical simulation within the dynamical triangulation approach to quantum gravity. Models I \& II suggest indeed an explanation of this mass dependence, in which the Schwarzschild scale plays a role. An estimate of the renormalized Newton coupling is made by matching with the small-mass region. Comparison of the dynamical triangulation results for mass renormalization with `renormalized perturbation theory' in the continuum leads to an independent estimate of this coupling, which is used in an improved analysis of the binding energy data.
gr-qc↗
Continuum interpretation of the dynamical-triangulation formulation of quantum Einstein gravity
In the time-space symmetric version of dynamical triangulation, a non-perturbative version of quantum Einstein gravity, numerical simulations without matter have shown two phases, with spacetimes that are either crumpled or elongated like branched polymers, with strong evidence of a first-order transition between them. These properties have generally been considered unphysical. Using previously unpublished numerical results, we give an interpretation in terms of continuum spacetimes that have constant positive and negative curvature, respectively in the 'elongated' and 'crumpled' phase. The magnitude of the positive curvature leads naturally to average spacetimes consisting solely of baby-universes in a branched-polymer structure, whereas the negative curvature accommodates easily a large mother universe, albeit with a crumpling singularity. Nevertheless, there is evidence for scaling in the crumpled phase, which we compare with the well-known scaling in the elongated phase. Using constraint effective-action models we analyze existing numerical susceptibility-data of the phase transition and determine the behavior of the average Regge-curvature. We propose a renormalization of the Regge curvature and compare it to the curvature of the above continuum spacetimes, and also to the curvature implied by the Gauss-Bonnet theorem in the continuum. The latter involves a more benign multiplicative renormalization and suggests that simulations at larger volumes are needed to settle the order of the phase transition.
hep-lat↗
Classical approximation to quantum cosmological correlations
We investigate up to which order quantum effects can be neglected in calculating cosmological correlation functions after horizon exit. As a toy model, we study $ϕ^3$ theory on a de Sitter background for a massless minimally coupled scalar field $ϕ$. We find that for tree level and one loop contributions in the quantum theory, a good classical approximation can be constructed, but for higher loop corrections this is in general not expected to be possible. The reason is that loop corrections get non-negligible contributions from loop momenta with magnitude up to the Hubble scale H, at which scale classical physics is not expected to be a good approximation to the quantum theory. An explicit calculation of the one loop correction to the two point function, supports the argument that contributions from loop momenta of scale $H$ are not negligible. Generalization of the arguments for the toy model to derivative interactions and the curvature perturbation leads to the conclusion that the leading orders of non-Gaussian effects generated after horizon exit, can be approximated quite well by classical methods. Furthermore we compare with a theorem by Weinberg. We find that growing loop corrections after horizon exit are not excluded, even in single field inflation.
hep-th↗
Simulations of Cold Electroweak Baryogenesis: Finite time quenches
The electroweak symmetry breaking transition may supply the appropriate out-of-equilibrium conditions for baryogenesis if it is triggered sufficiently fast. This can happen at the end of low-scale inflation, prompting baryogenesis to occur during tachyonic preheating of the Universe, when the potential energy of the inflaton is transfered into Standard Model particles. With the proper amount of CP-violation present, the observed baryon number asymmetry can be reproduced. Within this framework of Cold Electroweak Baryogenesis, we study the dependence of the generated baryon asymmetry on the speed of the quenching transition. We find that there is a separation between ``fast'' and ``slow'' quenches, which can be used to put bounds on the allowed Higgs-inflaton coupling. We also clarify the strong Higgs mass dependence of the asymmetry reported in a companion paper (hep-ph/0604263).
hep-ph↗
Simulations of Cold Electroweak Baryogenesis
We present real-time lattice simulations of Cold Electroweak Baryogenesis, in which the baryon asymmetry of the Universe is generated during tachyonic electroweak symmetry breaking at the end of inflation. In the minimal realisation of the model, only three parameters remain undetermined: the strength of CP-violation, the Higgs mass and the speed of the symmetry breaking quench. The dependence of the asymmetry on these parameters is studied.
hep-ph↗
Simulations of Cold Electroweak Baryogenesis: Dependence on Higgs mass and strength of CP-violation
Cold electroweak baryogenesis was proposed as a scenario to bypass generic problems of electroweak baryogenesis within the Standard Model. In this scenario, baryogenesis takes place during an electroweak symmetry breaking transition, which is also responsible for preheating after inflation. In the simplest modelling of the scenario, only two parameters remain undetermined: The Higgs mass and the strength of CP violation. Using full real-time lattice simulations, we compute the dependence of the asymmetry on these parameters.
hep-ph↗
Equilibration in phi^4 theory in 3+1 dimensions
The process of equilibration in phi^4 theory is investigated for a homogeneous system in 3+1 dimensions and a variety of out-of-equilibrium initial conditions, both in the symmetric and broken phase, by means of the 2PI effective action. Two Phi-derivable approximations including scattering effects are used: the two-loop and the ``basketball'', the latter corresponding to the truncation of the 2PI effective action at O(lambda^2). The approach to equilibrium, as well as the kinetic and chemical equilibration is investigated.
hep-ph↗
Chern-Simons and Winding Number in a Tachyonic Electroweak Transition
We investigate the development of winding number and Chern-Simons number in a tachyonic transition in the SU(2) Higgs model, motivated by the scenario of cold electroweak baryogenesis. We find that localized configurations with approximately half-integer winding number, dubbed half-knots, play an important role in this process. When the Chern-Simons number adjusts locally to the winding number, the half-knots can stabilize and acquire half-integer Chern-Simons number as well. We present two examples from numerical simulations: one half-knot that stabilizes early and one that gives rise to a late sphaleron transition. We also study the winding number distribution after the transition and present new results on the development of the Chern-Simons susceptibility.
hep-ph↗
Simulations of Cold Electroweak Baryogenesis
Cold Electroweak Baryogenesis is an attempt to explain the cosmological baryon asymmetry using only a minimal extension of the Standard Model. The relevant processes take place out of thermal equilibrium and are non-perturbative, and so must be studied using full, real-time lattice simulations. We present new results on the dependence on CP-violation and the Higgs-to-W-mass ratio
hep-lat↗
Simulations in Early Universe Theory
We give an impression of the type of results that have been obtained with numerical lattice simulations of field theory in the early universe.
hep-lat↗
Tachyonic preheating using 2PI-1/N dynamics and the classical approximation
We study the process of tachyonic preheating using approximative quantum equations of motion derived from the 2PI effective action. The O(N) scalar (Higgs) field is assumed to experience a fast quench which is represented by an instantaneous flip of the sign of the mass parameter. The equations of motion are solved numerically on the lattice, and the Hartree and 1/N-NLO approximations are compared to the classical approximation. Classical dynamics is expected to be valid, since the occupation numbers can rise to large values during tachyonic preheating. We find that the classical approximation performs excellently at short and intermediate times, even for couplings in the larger region currently allowed for the SM Higgs. This is reassuring, since all previous numerical studies of tachyonic preheating and baryogenesis during tachyonic preheating have used classical dynamics. We also compare different initializations for the classical simulations.
hep-ph↗
Cold Electroweak Baryogenesis
We present arguments that the CKM CP-violation in the standard model may be sufficient for the generation of the baryon asymmetry, if the electroweak transition in the early universe was of the cold, tachyonic, type after electroweak-scale inflation. A model implementing this is described which complies with the CMB constraints and which is falsifiable with the LHC. Numerical simulations of the tachyonic transition with an effective CP-bias indicate that the observed baryon asymmetry can be generated this way.
hep-ph↗
Effective CP violation in the Standard Model
We study the strength of effective CP violation originating from the CKM matrix in the effective action obtained by integrating out the fermions in the Standard Model. Using results obtained by Salcedo for the effective action in a general chiral gauge model, we find that there are no CKM CP-violating terms to fourth order in a gauge-covariant derivative expansion that is non-perturbative in the Higgs field. The details of the calculation suggest that, at zero temperature, the strength of CP violation is approximately independent of the overall scale of the Yukawa couplings. Thus, order of magnitude estimates based on Jarlskog's invariant could be too small by a factor of about 10^{17}.
hep-ph↗
Electroweak-scale inflation, inflaton-Higgs mixing and the scalar spectral index
We construct a phenomenological model of electroweak-scale inflation that is in accordance with recent cosmic microwave background observations by WMAP, while setting the stage for a zero-temperature electroweak transition as assumed in recent models of baryogenesis. We find that the scalar spectral index especially poses tight constraints for low-scale inflation models. The inflaton-Higgs coupling leads to substantial mixing of the scalar degrees of freedom. Two types of scalar particles emerge with decay widths similar to that of the Standard Model Higgs particle.
hep-ph↗
Baryon asymmetry from electroweak tachyonic preheating
We consider a scenario in which the baryon asymmetry was created in the early universe during a cold electroweak transition. The spinodal instability of the Higgs field caused by a rapid change of sign of its effective mass-squared parameter induces tachyonic preheating. We study the development of Chern-Simons number in this transition by numerical lattice simulations of the SU(2)-Higgs model with an added effective CP-violating term. A net asymmetry is produced, and we study its dependence on the size of CP violation and the ratio of Higgs to W mass.
hep-ph↗