Curvature effects in the spectral dimension of spin foams

Understand

It has been shown in [1] that a class of restricted spin foam models can feature a reduced spectral dimension of space-time.

• However, it is still an open question how curvature affects the flow of the spectral dimension.
• To answer this question, we consider another class of restricted spin foam models, so called spin foam frusta, which naturally exhibit oscillating amplitudes induced by curvature, as well as an extension of the parameter space by a cosmological constant.
• Numerically computing the spectral dimension of $1$-periodic frusta geometries using extrapolated quantum amplitudes, we find that quantum effects lead to a small change of spectral dimension at small scales and an agreement to semi-classical results at larger scales.