Building quantum space-time: spin foams and the renormalization group

• Applicant: Dr. Sebastian Steinhaus
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: since 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 422809950

Defining a consistent framework for gravity and quantum matter remains a fundamental puzzle in theoretical physics. We expect the solution to this vital question to lie in a theory of quantum gravity that describes space-time at smallest lengths, the Planck scale. Such a theory would give new insights into long standing questions, e.g. the origin of the universe in a Big Bang singularity.However the road towards a theory of quantum gravity is not clear. One promising candidate is spin foam gravity. In a nutshell, a spin foam is a path integral of space-time: instead of only considering a single geometry, all geometries are considered and weighted by an amplitude. To define this integral, space-time is divided into discrete “building blocks”, where the spin foam sums over all shapes and sizes of these blocks. Crucially, these models embrace a fundamental principle of general relativity, background independence: at no point is a reference to a fixed background geometry necessary.However, to unlock the full potential of spin foams and to transform them into a predictive theory I will address three interconnected key challenges in this project: identification of consistent models through renormalization, computability and extraction of observables to uncover the properties of quantum space-time.The subdivision of space-time into discrete building blocks is not unique, e.g. one can divide space-time into a few coarse or many fine building blocks. In general this fiducial choice significantly influences the results, yet which one, if any, gives the right result? I will tackle this riddle by background independent renormalization, where I relate spin foam amplitudes across discretizations such that the results are consistent. To turn this method into reality I will systematically implement truncations of spin foam theory space.To succeed at renormalization, I must study spin foams consisting of many building blocks, which makes numerical techniques indispensable. On the one hand, I will develop efficient algorithms to compute spin foam amplitudes in the deep quantum regime. On the other hand, I will spearhead the usage of Monte Carlo methods to unravel the renormalization group flow of spin foam models.Last but not least I will define and study observables to reveal the properties of quantum space-time. I will examine spin foams themselves by computing their curvature and their spectral dimension. The latter is an effective dimension measure dependent on scale. Moreover, I will tackle the vital question of coupling matter to quantum space-time. Ultimately I aim for discovering the mutual renormalization group of spin foams and matter. This part of the project is particularly crucial since it will allow me to compare spin foam gravity to other approaches of quantum gravity. Furthermore, it might open the door towards phenomenology.

• DFG Programme: Independent Junior Research Groups