Research Projects
The group’s current projects turn broad questions about quantum fields, spacetime and gravity into focused research programmes. They investigate the symmetries and phases of quantum theories, connections between field theory and gravity, and possible quantum structures of spacetime. The entries below present each project’s aims and the funding that supports it.
Minimal Covariant Quantum Spacetime in Matrix Theory
Project leader: Harold Steinacker
Date: 01.09.2026 - 31.08.2029
Principal Investigator Project
This project investigates an explicit realization of quantum spacetime within Matrix Theory, which is one candidate for a fundamental quantum theory including gravity. It aims to explore how near-realistic spacetime geometry and covariance can emerge from the underlying matrix degrees of freedom. A particular focus is on the resulting gravity theory, its relation or deviation from general relativity, and the resolution of singularities which arise within general relativity.
Funded by: FWF
“Minimal Covariant Quantum Spacetime in Matrix Theory” @FWF
Defects in low-dimensional TQFTs
Project leader: Mulevicius Vincentas
Date: 01.12.2024 - 30.11.2027
ESPRIT Program
Quantum field theory (QFT) is one of the most successful frameworks for describing the fundamental interactions of nature, but its mathematical foundations remain difficult to formulate rigorously. Functorial quantum field theory provides a conceptual framework based on category theory, relating the geometry of spacetime to algebraic structures. Topological quantum field theories (TQFTs) are particularly well suited to this approach, as they focus on properties of spacetime that are invariant under continuous deformations.
This project investigates TQFTs using the functorial approach, with a particular focus on defects—special regions of spacetime that can represent particles, strings, or branes. It studies how new physical theories can emerge when spacetime is densely filled with such defects, as well as the role of extra dimensions in these emergent theories. The methods may also have applications to topological phases of matter and quantum computing.
Funded by: FWF
Defects in low-dimensional TQFTs @FWF
A Hamiltonian term constructed from defects in 3D theory
Fundamental challenges in theoretical physics (THEORY-CHALLENGES)
Fredenhagen Stefan, Carqueville Nils
Date: 10.10.2023 - 09.10.2027
COST Action (Action Chair: Alessandro Sfondrini)
Physicists can model a wide range of physical systems with remarkable accuracy, but many theoretical approaches rely on weak interactions and fail for strongly interacting systems. This Action aims to develop new methods for studying such systems by exploiting symmetries, dualities, and theoretical consistency.
It will bring together researchers in theoretical and mathematical physics, including quantum field theory, string theory, gravity, geometry, and information theory, creating a European network for collaboration. The Action will also promote public and school outreach to improve the understanding and perception of theoretical physics and scientific research.
Stefan Fredenhagen is part of the Management Committee, Nils Carqueville is the leader of Working Group 3, “Low-dimensional systems”, part of the Management Committee as well as member of the Core Group.
Funded by: COST (European Cooperation in Science and Technology)
Fundamental challenges in theoretical physics @COST
Higher defect state sum models
Project leader: Carqueville Nils
Date: 01.10.2023 - 30.04.2028
Principal Investigator Project
Quantum field theory is a central part of a modern understanding of physics, especially elementary particle physics and condensed matter physics. A full understanding would also involve a mathematically rigorous and conceptually clear formulation of quantum field theory. The search for this has been a goal of both theoretical physics and pure mathematics for several decades. Our project is part of this endeavour, aiming for a functorial description of so-called topological state sum models. To achieve this, ideas and results of theoretical physics, category theory and algebraic topology are to be employed to construct a general theory of state sum models as an iterative phenomenon that consistently reduces higher-dimensional aspects to lower-dimensional ones. Moreover, this theory will be applied to establish new relations between known topological quantum field theories, to further develop the representation theory of higher algebras, and to describe anomalies of 3-dimensional theories.
Funded by: FWF
Higher defect state sum models @FWF
Phases of quantum field theories: symmetries and vacua
Project leader: Marcus Sperling
Date: 1.10.2023 - 30.09.2028
FWF START Award
This project investigates quantum field theories using supersymmetric models as a controlled setting to study their quantum properties. It focuses on quantum vacua and symmetries, with the aim of classifying new types of quantum vacua in six-dimensional theories, understanding their underlying mathematical structures, and applying these insights to four-dimensional quantum field theories. The project will contribute to both theoretical physics and mathematics by providing new insights into quantum phenomena and geometric structures.
Funded by: FWF
Phases of quantum field theories: symmetries and vacua @FWF