Kaehler-Dirac fermions and random geometries
This event is part of the HET Seminar Series.
The Kaehler-Dirac equation offers an alternative to the Dirac equation for the description of fermions. It has the advantage that it does not require the introduction of a vielbein and spin connection on curved spacetimes. Furthermore it admits a simple discretization on such spaces that circumvents the usual fermion doubling problem. I will show that Kaehler Dirac fermions exhibit an anomaly which is determined by the topology of the background space and that this anomaly can be computed exactly on a triangulation of that space. This gives rise to a non-zero fermion condensate whose value is determined only by the volume of the space. I will also present results for the meson spectra of such theories in candidate theories of quantum gravity based on performing a discrete path integral over triangulated geometries. The results of these studies support the existence of a continuum limit for these models.