Multifractional theories: an unconventional review

Understand

We answer to 72 frequently asked questions about theories of multifractional spacetimes.

• Apart from reviewing and reorganizing what we already know about such theories, we discuss the physical meaning and consequences of the very recent flow-equation theorem on dimensional flow in quantum gravity, in particular its enormous impact on the multifractional paradigm.
• We will also get some new theoretical results about the construction of multifractional derivatives and the symmetries in the yet-unexplored theory $T_\gamma$, the resolution of ambiguities in the calculation of the spectral dimension, the relation between the theory $T_q$ with $q$-derivatives and the theory $T_\gamma$ with fractional derivatives, the interpretation of complex dimensions in quantum gravity, the frame choice at the quantum level, the physical interpretation of the propagator in $T_\gamma$ as an infinite superposition of quasiparticle modes, the relation between multifractional theories and quantum gravity, and the issue of renormalization, arguing that power-counting arguments do not capture the exotic properties of extreme UV regimes of multifractional geometry, where $T_\gamma$ may indeed be renormalizable.
• A careful discussion of experimental bounds and new constraints are also presented.