Symmetries in Quantum Gravity

Throughout the history of physics symmetries have played a pivotal role.

In recent years our understanding of them has been revolutionized to include their action on extended, rather than point-like, operators, called generalized symmetries. So far, however, they have mainly been discussed in theories without gravity.

In this project I will take on this important challenge and derive universal constraints on theories of quantum gravity with generalized symmetries.

This combination of generalized symmetries and universal properties of gravitational systems allows to utilize the remarkable recent progress in both fields to provide insights into the hitherto unknown laws of quantum gravity, their manifestation in our Universe, and their implications at low energies.

Applying these new laws to supersymmetric theories, I will show that all consistent low-energy supergravity theories necessarily have a string theory origin.

I will further apply the constraints to restrict phenomenological models describing the dynamics of Nature.The key strategy of my proposal is to investigate the gauging and explicit breaking of generalized symmetries, required by the absence of global symmetries in quantum gravity. Gauging demands the absence of anomalies, which would break the symmetries via quantum effects.

I will classify these for generalized symmetries including the presence of quantum gravity fluctuations of the underlying spacetime manifold.

The breaking of symmetries requires the inclusion of new objects, whose structure, properties, and applications I will explore systematically.Both, the classification of these general anomalies as well as the classification of symmetry-breaking objects uses the mathematical formalism of bordism groups.

Generalizing these to include localized degrees of freedom, SymQuaG uncovers a full web of novel anomalies in order to derive universal consistency constraints, which are then tested in the laboratory of string theory and beyond.