Spectral dimensions from the spectral action

Understand

The generalised spectral dimension $D_{ S}(T)$ provides a powerful tool for comparing different approaches to quantum gravity.

• In this work, we apply this formalism to the classical spectral actions obtained within the framework of almost-commutative geometry.
• Analysing the propagation of spin-0, spin-1 and spin-2 fields, we show that a non-trivial spectral dimension arises already at the classical level.
• The effective field theory interpretation of the spectral action yields plateau-structures interpolating between a fixed spin-independent $D_{ S}(T) = d_S$ for short and $D_{ S}(T) = 4$ for long diffusion times $T$.