Description du projet
Accéder à des problèmes autrement insolubles: nouveaux résultats exacts pour les symétries brisées
La physique moderne s’appuie fortement sur des considérations de symétrie; la symétrie faisant référence à l’invariance sous certaines transformations. En d’autres termes, le système est identique après une certaine transformation. Cependant, la symétrie n’est pas toujours «exacte» ou inconditionnellement valide; elle peut être «brisée», ce qui signifie que le système après la transformation se caractérise par une symétrie inférieure à celle du système d’origine. D’importants progrès ont été réalisés en ce qui concerne les théories à forte symétrie, mais pas pour les théories plus réalistes dans lesquelles la symétrie est brisée. Le projet BrokenSymmetries, financé par le CER, comblera cette lacune en développant de nouveaux résultats exacts pour des cas dans lesquels certaines supersymétries ou invariances conformes sont brisées.
Objectif
Symmetries serve as our main guide in studying physical phenomena. The more symmetric a system is, the more constrained are its degrees of freedom and the better prospects we have to understand and solve it. Significant progress has been achieved in the study of theories with high amounts of symmetry in the last decades. Supersymmetry and conformal invariance are the main reasons why the beautiful idea of holography materialised into the AdS/CFT correspondence and the discovery of hidden symmetries (integrability) in gauge theories was possible. Thanks to supersymmetry, modern mathematical techniques allowed the evaluation of the otherwise unfathomable path integral and the comprehensive study of a long list of physical observables. Finally, the successful revival of the conformal Bootstrap program is based on conformal invariance.
These breakthroughs are, unfortunately, applicable only to theories with unrealistic amounts of symmetry. BrokenSymmetries will break this impasse by applying the aforementioned ideas to more realistic theories, where some of the supersymmetry and/or conformal invariance are broken.
The key innovation of BrokenSymmetries is to still make use of a broken symmetry. Symmetries are captured by Ward identities which we can still derive in various cases of symmetry breaking. Broken symmetries also imply powerful non-perturbative relations that observables obey. We will combine these with the developments mentioned above, producing novel exact results. Our approach will give a handle on otherwise insoluble problems.
The objectives of BrokenSymmetries are to obtain exact results while breaking:
1) conformal invariance spontaneously, keeping supersymmetry intact;
2) supersymmetry explicitly, keeping conformal invariance intact;
3) both supersymmetry and conformal invariance turning on the temperature;
4) (super)symmetry generators in the context of integrability, which get upgraded to quantum groups' generators.
Champ scientifique
Programme(s)
- HORIZON.1.1 - European Research Council (ERC) Main Programme
Régime de financement
ERC - Support for frontier research (ERC)Institution d’accueil
22607 Hamburg
Allemagne