Spectral dimension on spatial hypersurfaces in causal set quantum gravity

Understand

An important probe of quantum geometry is its spectral dimension, defined via a spatial diffusion process.

• In this work we study the spectral dimension of a ``spatial hypersurface'' in a manifoldlike causal set using the induced spatial distance function.
• In previous work, the diffusion was taken on the full causal set, where the nearest neighbours are unbounded in number.
• The resulting super-diffusion leads to an increase in the spectral dimension at short diffusion times, in contrast to other approaches to quantum gravity.