Fermions with no fundamental charges call for extra dimensions

TL;DR

This paper argues that in theories with fermions carrying no fundamental charges and interacting only via gravity, only certain spacetime dimensions are consistent with mass protection, notably excluding most dimensions except specific cases.

Contribution

It identifies specific spacetime dimensions compatible with fermions without fundamental charges under gravity-only interactions, refining constraints on higher-dimensional theories.

Findings

Dimensions 4, 12, 20,... are excluded for such fermions.

Only dimensions d=2 mod 4 remain acceptable with multiple families.

Most higher dimensions are incompatible with mass protection in this scenario.

Abstract

We call attention to that if assuming no conserved charges in the fundamental theory with fermions, which carry only a spin and interact with only the gravity, the dimensions $4, 12, 20,.....,$ as well as all odd dimensions, are excluded under the requirement of mass protection. If more than one family is required, than only dimensions d=2 (mod 4) remains as acceptable, since then other by 4 devisable dimensions are excluded.