Project description
Accessing otherwise unsolvable problems: novel exact results for broken symmetries
Modern physics relies heavily on symmetry considerations, where symmetry refers to invariance under certain transformations. In other words, the system looks the same after some transformation. However, symmetry is not always ‘exact’ or unconditionally valid; it can be ‘broken’, meaning the system after the transformation is characterised by a lower symmetry than the original one. Considerable progress has been made regarding theories with high amounts of symmetry, but not for more realistic theories in which symmetry is broken. The ERC-funded BrokenSymmetries project will address this gap by developing novel exact results for cases in which some of the supersymmetry and/or conformal invariance are broken.
Objective
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.
Fields of science
Programme(s)
- HORIZON.1.1 - European Research Council (ERC) Main Programme
Funding Scheme
ERC - Support for frontier research (ERC)Host institution
22607 Hamburg
Germany