Bordisms in Quantum Gravity

by Markus Dierigl (LMU Munich)

Thursday 19 Jun 2025, 16:15 → 17:15 Europe/Berlin

DESY

In this talk I will present an introduction to the use of bordism groups in theories of quantum gravity. Bordism groups classify the deformation classes of manifolds with a fixed structure (e.g. orientation, Spin, or the presence of gauge fields). Their first application determines a phase ambiguity of theories under topology changes of the underlying spacetime manifolds and is associated to a certain class of quantum anomalies. The second application associates conserved topological charges to non-trivial deformation classes. Since it is believed that quantum gravity does not allow for global symmetries such a charge conservation must be broken by the introduction of (new) dynamical, symmetry-breaking objects which become part of the quantum gravity theory at high energies. I will then illustrate that these general applications lead to surprises even for well-understood theories such as type IIB supergravity in ten dimensions.