François Englert

The Creation of the Universe as a Quantum Phenomenon

Quantum creation of massy particles can occur in the cosmological context without cost of energy. This fact is seized upon to construct a causal open homogeneous isotropic cosmology. The universe is conceived as the response of matter and the gravitational field to a spontaneous pointlike disturbance. Its history unfolds in two stages, creation and free expansion. The first stage gives rise to a “fireball.” The free expansion is extrapolated back to the “fireball.” The latter thus replaces the “big-bang,” thereby avoiding an initial singularity. Though not intrinsic to the theory it does suggest the interpretation of the cosmological part of the gravitational field as the scalar dilaton that is encountered in the dynamical generation of mass in conformally invariant theory.

Gauged N = 8 supergravity and its breaking from spontaneous compactification

Abstract Gauged N = 8 supergravity emerges from spontaneous compactification of eleven-dimensional supergravity on the riemannian S 7 . This is the only non-trivial compactification scheme preserving full symmetry. The four-dimensional theory admits a spontaneously broken solution describable as a compactification on the parellelized S 7 ; supersymmetry is completely broken and the local SO(8) group is reduced to G 2 .

The fluctuating seven-sphere in eleven-dimensional supergravity

Abstract The full bosonic spectrum of eleven-dimensional supergravity compactified on the seven-sphere is obtained. The spectrum agrees with OSp(4|8) supersymmetry despite the appearance of 294 massless scalars which are not members of the N=8 massless supermultiplet. Negative (mass)2 arises only in the scalar sector with 112 nodes whose common (mass)2 is equal to the threshold value for background stability.

Conformal invariance in quantum gravity

Abstract Trace anomalies in a conformal invariant theory do not arise when its conformal invariance in four dimensions is extended to an arbitrary number n of space-time dimensions: the theory can be made finite in any order of perturbation theory by conformal invariant counterterms in n dimensions. Such an extension of conformal invariance is possible provided one works in the framework of spontaneously broken conformal invariance. This is shown explicitly by working out several examples at the one-loop level and by examining the Ward identities which lead to a general proof. We speculate upon possible consequences of these results on the nature of gravitation and other fundamental interactions.

The symmetry of M-theories

We consider the Cartan subalgebra of any very extended algebra Script G+++ where Script G is a simple Lie algebra and let the parameters be space-time fields. These are identified with diagonal metrics and dilatons. Using the properties of the algebra, we find that for all very extensions Script G+++ of simple Lie algebras there are theories of gravity and matter, which admit classical solutions carrying representations of the Weyl group of Script G+++. We also identify the T and S-dualities of superstrings and of the bosonic string with Weyl reflections and outer automorphisms of well-chosen very extended algebras and we exhibit specific features of the very extensions. We take these results as indication that very extended algebras underlie symmetries of any consistent theory of gravity and matter, and might encode basic information for the construction of such theory.

Chiral symmetry breaking in the action formulation of lattice gauge theory

Abstract We show, in the euclidean path-integral formulation of strong-coupling lattice gauge theory, that continuous chiral symmetry is dynamically broken, and obtain the standard current algebra result that m pseudo-Goldstone 2 ∼ m quark 〈 ψ ψ〉 . We also remark that the center of the gauge group does not seem very relevant for this result; chiral symmetry breaking is a property of strong-coupling lattice theories both in the case where quark color is confined, and also in the case where it is screened by gauge field fluctuations.

The Mass Spectrum of Supergravity on the Round Seven Sphere

Abstract We derive the mass spectrum of supergravity compactified on the round seven-sphere. The final result may be arrived at either by employing harmonic expansions on S7 or by using properties of Osp(8,4).

The causal universe

Creation of matter is possible in the cosmological context, without cost of energy. This creation is regulated by the laws of quantum mechanics and general relativity. These elements are used to conceive a singularity-free causal open homogeneous isotropic cosmology. The history of the universe unfolds in two stages: the “fireball” production stage, which occurs as the response to a spontaneous local disturbance, is followed by free expansion. The latter extrapolates back to the former to avoid the initial “big-bang” singularity.

Supersymmetry breaking by torsion and the Ricci-flat squashed seven-spheres

Abstract In eleven-dimensional supergravity, unbroken supersymmetries may survive spontaneous compactification to V 4 × V 7 only for Freund-Rubin solutions to the equations of motion. A torsion which renders V 7 Ricci-flat and breaks supersymmetry can then be induced spontaneously. Two squashed seven-spheres with torsion are obtained in this way: the flattening torsion components are constant and given by the octonion multiplication table.

Cosmogenesis and the origin of the fundamental length scale

The creation of the universe is regarded as a self-consistent process in which matter is engendered by the space-time varying cosmological gravitational field and vice versa. Abundant production can occur only if the mass of the particles so created is of the order of the Planck mass (= κ−12. We conjecture that this is the origin of the fundamental length scale in field theory, as it is encountered, for example, in present efforts towards grandunification. The region of particle production is steady state in character. It ceases when the produced particles decay. The geometry of this steady state is characteristic of a de Sitter space. It permits one to estimate the number of ordinary particles presently observed, N. We find log N = O (mτdecay) = O(g−2) = O(102), with the usual estimate of g = O(10− at the Planck length scale. This is not inconsistent with the experimental estimate N ⋍ O(1090). After production, cosmological history gives way to the more conventional scheme of free expansion. The present paper is a self-contained account of our view of cosmological history and the production of matter in a varying gravitational field. Special care has been taken to describe the vacuum correctly in the present context and to perform the necessary subtractions of zero-point effects.