Generalized symmetries and F-theory

• Applicant: Dr. Markus Dierigl
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: from 2019 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 418272994

Symmetry is one of the main guiding principles in (theoretical) physics. It appears in two different guises. Gauge symmetries represent redundancies in the description of the theory and have to be accounted for to allow for sensible predictions. In turn they lead to the fundamental interactions of nature. Global symmetries are physical and account for the properties of states in quantum systems. They further classify the phase structure of theories. Recently the concept of global symmetries has been generalized fundamentally. This led to new insights in the structure of confining four-dimensional gauge theories such as the strong interactions. Since these theories are hard to study directly due to their strong coupling, these generalized (global) symmetries are a powerful extension of our understanding of the interactions observed in nature.An important difference between gauge and global symmetries arises when the theory is coupled to gravity. While gauge symmetries can be present in gravitational theories, global symmetries are argued to be consistent only in the absence of gravity. These arguments are based on the quantum nature of black holes and gravity itself. Consistency constraints for gravitational theories have been under intense investigation recently and have led to various interesting results, among which are restrictions on models of inflation in the early phase of our universe as well as the nature and masses of neutrinos. However, since these criteria arise from the quantum nature of gravity their investigation demands a consistent theory of quantum gravity. String theory is such a framework.String theory is efficiently (and non-perturbatively) realized in so-called F-theory. In F-theory many of the physical properties of the model are encoded in geometrical objects, which allows for the application of powerful mathematical tools such as algebraic geometry and leads to improved computational possibilities. Moreover, F-theory intrinsically contains the possibility to decouple gravity in a controllable way and thus is well-suited for an investigation of the interplay between gravity and generalized (global) symmetries.The subject of our project is the realization and investigation of generalized (global) symmetries in the context of F-theory. A first step is to identify the geometrical realization of generalized global symmetries in F-theory models without gravity. This opens up the possibility to construct different phases of matter in this controllable setup and enriches our theoretical control in the strong-coupling regime. Consecutively, we couple the theories to gravity and study the fate of generalized symmetries in this consistent framework of quantum gravity. Ultimately, we can extract additional consistency constraints for gravitational theories including generalized symmetries and apply them to phenomenologically interesting models, deepening our understanding of the quantum nature of gravity.

• DFG Programme: Research Fellowships
• International Connection: USA
• Host: Professorin Dr. Mirjam Cvetic