Research & Publications

Quantum field theory and gravity provide powerful descriptions of fundamental physics, yet they leave deep questions about the structure of quantum theories and the nature of spacetime. The Mathematical Physics group at the University of Vienna studies these questions through symmetry and geometry, drawing on ideas from algebra, topology and theoretical physics. We seek both a clearer understanding of existing theories and new frameworks in which their connections become visible.

Our work on quantum field theory includes topological, conformal and supersymmetric theories. In topological field theory, defects and orbifold constructions shed light on generalized symmetries and topological phases. Supersymmetric theories offer a setting in which strongly interacting phenomena can be studied with precise tools, including the geometry of vacua, the structure of phases and descriptions using magnetic quivers. Conformal field theories connect these questions to another theme of the group: the relation between quantum fields and gravity.

We investigate that relation through higher-spin gravity and holography. Higher-spin theories extend familiar gravitational and gauge theories, while holography reveals connections to conformal field theories. We also study non-Lorentzian geometries and field theories, including Carrollian structures, to explore alternative notions of spacetime symmetry and their relation to flat-space holography. Matrix models offer a complementary approach to the quantum nature of spacetime: we investigate how geometry and gravity might emerge from underlying quantum degrees of freedom, and develop the mathematical tools needed to describe them.

Across these subjects, mathematical structures are both tools of investigation and part of what we aim to understand. The group brings complementary perspectives to shared questions about quantum fields, spacetime and gravity.