Francois Englert

G+++ Invariant formulation of gravity and M-theories: exact intersecting brane solutions

The set of exact solutions of the non-linear realisations of the +++ Kac-Moody algebras is further analysed. Intersection rules for extremal branes translate into orthogonality conditions on the positive real roots characterising each brane. It is proven that all the intersecting extremal brane solutions of the maximally oxidised theories have their algebraic counterparts as exact solutions in the +++-invariant theories. The proof is extended to include the intersecting extremal brane solutions of the exotic phases of the maximally oxidised theories.

From very-extended to overextended gravity and M-theories

The formulation of gravity and M-theories as very-extended Kac-Moody invariant theories encompasses, for each very-extended algebra G+++, two distinct actions invariant under the overextended Kac-Moody subalgebra G++. The first carries a euclidean signature and is the generalisation to G++ of the E10-invariant action proposed in the context of M-theory and cosmological billiards. The second action carries various Lorentzian signatures revealed through various equivalent formulations related by Weyl transformations of fields. It admits exact solutions, identical to those of the maximally oxidised field theories and of their exotic counterparts, which describe intersecting extremal branes smeared in all directions but one. The Weyl transformations of G++ relates these solutions by conventional and exotic dualities. These exact solutions, common to the Kac-Moody theories and to space-time covariant theories, provide a laboratory for analysing the significance of the infinite set of fields appearing in the Kac-Moody formulations.

The hidden horizon and black hole unitarity

We motivate through a detailed analysis of the Hawking radiation in a Schwarzschild background a scheme in accordance with quantum unitarity. In this scheme the semi-classical approximation of the unitary quantum — horizonless — black hole S-matrix leads to the conventional description of the Hawking radiation from a classical black hole endowed with an event horizon. Unitarity is borne out by the detailed exclusive S-matrix amplitudes. There, the fixing of generic out-states, in addition to the in-state, yields in asymptotic Minkowski space-time saddle-point contributions which are dominated by Planckian metric fluctuations when approaching the Schwarzschild radius. We argue that these prevent the corresponding macroscopic “exclusive backgrounds” to develop an event horizon. However, if no out-state is selected, a distinct saddle-point geometry can be defined, in which Planckian fluctuations are tamed. Such “inclusive background” presents an event horizon and constitutes a coarse-grained average over the aforementioned exclusive ones. The classical event horizon appears as a coarse-grained structure, sustaining the thermodynamic significance of the Bekenstein-Hawking entropy. This is reminiscent of the tentative fuzzball description of extremal black holes: the role of microstates is played here by a complete set of out-states. Although the computations of unitary amplitudes would require a detailed theory of quantum gravity, the proposed scheme itself, which appeals to the metric description of gravity only in the vicinity of stationary points, does not.

The Brout-Englert-Higgs Mechanism and Its Scalar Boson

The Brout-Englert-Higgs (BEH) mechanism extending spontaneous symmetry breaking to gauge fields had a considerable impact on both theoretical and experimental elementary particle physics. It is corroborated by the discovery of the Z and the W, and by the precision electroweak tests. The recent detection by the LHC at CERN of a particle identifiable to its massive BEH scalar boson not only constitutes a direct verification of the mechanism, but detailed analysis of its different decay processes may yield indications on the world hitherto hidden beyond the Standard Model. These topics are discussed with emphasis on conceptual issues. [Editors note: for a video of the talk given by Prof. Englert at the Aharonov-80 conference in 2012 at Chapman University, see quantum.chapman.edu/talk-2.]