On the failure of spin–statistics connection in quantum gravity

Many years ago Friedman and Sorkin [Phys. Rev. Lett. 44 (1980) 1100; Gen. Rel. Grav. 14 (1982) 615] established the existence of certain topological solitonic excitations in quantum gravity called (topological) geons. Geons can have quantum numbers like charge and can be tensorial or spinorial having integer or half-odd integer spin. A striking result is that geons can violate the canonical spin–statistics connection. Such violation induces novel physical effects at low energies. The latter will be small since the geon mass is expected to be of the order of Planck mass. Nevertheless, these effects are very striking and include CPT and causality violations and distortion of the cosmic microwave spectrum. Interesting relations of geon dynamics to supersymmetry are also discussed.