Descrizione del progetto
Accesso a problemi altrimenti irrisolvibili: nuovi risultati esatti per le simmetrie rotte
La fisica moderna si basa molto su considerazioni di simmetria, dove per simmetria si intende l’invarianza a fronte di determinate trasformazioni; in altre parole, il sistema appare identico dopo alcune trasformazioni. Tuttavia, la simmetria non è sempre «esatta» o incondizionatamente valida, ma può essere «rotta», il che significa che il sistema dopo la trasformazione è caratterizzato da una simmetria inferiore a quella originale. Sono stati fatti notevoli progressi per quanto riguarda le teorie con elevate quantità di simmetria, ma non per le teorie più realistiche in cui la simmetria è rotta. Il progetto BrokenSymmetries, finanziato dal CER, affronterà questa lacuna elaborando nuovi risultati esatti per i casi in cui alcune delle supersimmetrie e/o invarianze conformi sono rotte.
Obiettivo
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.
Campo scientifico
Programma(i)
- HORIZON.1.1 - European Research Council (ERC) Main Programme
Argomento(i)
Meccanismo di finanziamento
ERC - Support for frontier research (ERC)Istituzione ospitante
22607 Hamburg
Germania