Research
General Framework
The standard model of particle physics is based on quantum field theory, a framework that reconciles Poincaré invariance with quantum mechanics and allows one to understand the electromagnetic and the two types of nuclear interactions. The fourth fundamental interaction, gravitation, is described by Einstein's theory of general relativity. Although the standard model and general relativity explain a remarkable range of experiments and observations, theoretical arguments indicate that neither of them can be complete. The standard model of particle physics contain a large number of parameters and somewhat ad hoc terms, while Einstein theory of general relativity appears to be in conflict with the principles of quantum mechanics.
Purely theoretical attempts at generalisations are constrained, of course, by mathematical consistency and the need to incorporate the previous theories in the domains where they have been successful. Additional guiding principles are needed, though. Symmetry is such a principle and pervades most of the research carried out in theoretical high energy physics.
The Yang-Mills type theories for the three microscopic forces of elementary particle physics are invariant under Poincaré symmetries, the symmetry group of flat space-time. These theories admit in addition certain internal symmetries known as gauge symmetries. In general relativity, gravitation arises when going from a flat to a curved spacetime, and Poincaré symmetries become part of the gauge group of diffeomorphisms.
In models that go beyond the existing theories, other symmetries come to the front.
(i) Supersymmetry:
Supersymmetry is a natural extension of Poincaré symmetry in the presence of fermionic matter fields. Supersymmetric extensions of the standard model will be tested at the experiments planned in the Large Hadron Collider at CERN in Geneva.
Supersymmetry is also an important ingredient of string theory, a model for unification of the four fundamental interactions and for a microscopic formulation of gravity. At low energy, higher dimensional theories of gravitation emerge that include supersymmetry as part of their gauge group together with supersymmetric extensions of Yang-Mills gauge theories.
(ii) Dualities:
One of the first theoretical extensions of Maxwell's theory of electromagnetism has been the inclusion of magnetic sources. The introduction of such sources is motivated by the desire to preserve invariance under duality rotations, a symmetry of the source-free equations. The solution that is dual to the Coulomb solution describing a static point-particle electron is a magnetic monopole. In some sense, black hole solutions in gravitational theories are the analogue of the Coulomb solution to Maxwell's theory.
In nonlinear theories like Yang-Mills theories, dualities relate a strongly coupled regime to one at weak coupling, where standard perturbative computations may be performed. In supersymmetric situations, these dualities become tractable. Finally, dualities between different string theories as well as holographic duality between gauge and gravity theories feature prominently in most of the recent developments in string theory.
(iii) Hidden symmetries:
Hidden symmetries in gravity and string theory arise in compactifications of supergravity theories and among the string duality groups. The algebraic structure of these symmetries is related to infinite-dimensional Lorentzian Kac-Moody algebras, in particular those of E10 and E11.
Research carried out in the group "Physique Mathématique des Interactions fondamentales":
Since consequences of supersymmetry are not observed at energy scales that are presently accessible, an important theoretical question is how supersymmetry is broken at low energy scales. Part of the research carried out is devoted to dynamical supersymmetry breaking, i.e., supersymmetry breaking at the non-perturbative level. More specifically, we construct supersymmetry breaking models with relevant gauge sectors and analyse their coupling to gravity. Their embedding in full-fledged string theory realisations is studied.
Another research subject in our group is the study of non-perturbative properties of Yang-Mills theories. The Strong Force generated by the Yang-Mills interactions is so intense that the associated energy field is responsible for about 90% of the mass of ordinary matter. However, due to the strong coupling, the standard perturbative methods of quantum field theory do not apply and other approaches, able to deal with non-linear effects, must be used. We follow two main routes in this direction. The first one is to derive and interpret exact non-perturbative results using special properties of supersymmetric theories. We have developed a first-principle approach based on the intanton calculus from which the fully quantum landscape of vacua, which corresponds to certain algebraic varieties, can be derived. A second route is to use the gauge/string duality, which allows to reformulate the Yang-Mills theories in terms of certain string theories. In many cases, the string formulation yields a simple and natural description of strongly quantum gauge theoretic effects. Moreover, this approach establishes an equivalence between theories with no gravity (the Yang-Mills theories) and theories with gravity (the string theories). This correspondence and its generalizations is one of our best hope to understand both the Strong Force and the quantum properties of gravitation.
Another part of our research effort concerns electromagnetic and gravitational dualities. In this context, we study black holes, monopoles in the presence of gravity and the Taub-NUT spacetime, the gravitational analogue of the magnetic monopole.
Hidden symmetries are a major research theme of our group. In particular, we study how these symmetries emerge in the context of the BKL limit of supergravity theories, i.e., near a spacelike singularity and we use them in order to generate new solutions of 11 dimensional supergravity.
The group has a long standing interest in general problems related to systems with gauge invariance and techniques used for their quantisation.
More details can be found on the homepages of the group members.