A scale at 10 MeV, gravitational topological vacuum, and large extra dimensions

Understand

We discuss a possible scale of gravitational origin at around $10$ MeV, or $10^{-12}$ cm, which arises in the MacDowell-Mansouri formalism of gravity due to the topological Gauss-Bonnet term in the action, as pointed out by Bjorken several years ago.

• A length scale of the same size emerges also in the Kodama solution in gravity, which is known to be closely related to the MacDowell-Mansouri formulation.
• We particularly draw attention to the intriguing incident that existence of six compact extra dimensions originated from TeV-scale quantum gravity as well points to a length scale of $10^{-12}$ cm, as the compactification scale.
• The presence of six such extra dimensions is also in remarkable consistency with the MacDowell-Mansouri formalism; it provides a possible explanation for the factor of $\sim10^{120}$ multiplying the Gauss-Bonnet term in the action.