Quantum gravity, string theory and symmetries
Perhaps the greatest challenge of modern theoretical physics is the quantization of the gravitational field. A consistent theory of quantum gravity seems to be required to answer questions about the early universe and the nature of black holes. Several candidate theories have been put forward over the last decades. On the one hand, supergravity and superstring theory aim for a unification of gravity with the other fundamental interactions, and have their roots in QFT. On the other hand, non-perturbative approaches such as loop quantum gravity, spin foams and group field theory proceed from basic principles of General Relativity (GR). The first core area concerns the underlying structures and symmetries of these different theories, with the aim of distilling the crucial physical and mathematical objects for the correct formulation of quantum gravity.
Both supergravity and string theory possess remarkable symmetries that are, however, not always manifestly realized. In order to understand their geometrical origin, so-called "exceptional geometries" are being developed that merge the conventional differential geometry underlying Einstein's theory with the symmetries in the matter sector. In addition, the analysis of the differential equations governing supergravity in the vicinity of cosmological singularities has revealed the presence of infinite-dimensional symmetry algebras. The study of these symmetries has led to many novel insights, and is expected to have important consequences for quantization; ultimately, it could even provide a fully algebraic reformulation of quantum gravity with emergent space-time.
These symmetries are also closely related to the duality symmetries known to arise in compactifications of string theory which allow sometimes the full determination of the observables (including non-perturbative contributions in an elegant way). Crucial aspects of this intriguing connection remain to be explored in future work, and may for instance shed new light on various questions related to black hole entropy. Important insights into the structure of both quantum gravity and QFT are also due to the string/gauge theory duality or AdS/CFT duality. The focus of the IMPRS here will be on exact results and on the hidden integrability structures. Investigations both at strong coupling, employing string theory, as well as weak coupling, employing supersymmetric gauge theory, are envisaged. The string/gauge correspondence also has important applications in standard QCD. Phenomenological questions relating to perturbative quantum gravity as an effective field theory and Higgs physics will be studied as well.
The IMPRS will also pursue research on higher spin (s>2) gauge theories, following up on recent progress in overcoming obstacles in formulating an interacting theory of this type. This is a very active area of current research, with many new applications also for the AdS/CFT correspondence. The AEI has been one of the leaders in this research direction. Understanding the connection between massive string states and the higher spin gauge symmetries will be a major open topic to be investigated in the IMPRS.