Constraints on discrete global symmetries in quantum gravity

The question whether global symmetries can be realized in quantum-gravity-matter-systems has far-reaching phenomenological consequences. Here, we collect evidence that within an asymptotically safe context, discrete global symmetries of the form Z(n), n > 4, cannot be realized in a near-perturbative regime. In contrast, an effective-field-theory approach to quantum gravity might feature such symmetries, providing a mechanism to generate mass hierarchies in the infrared without the need for additional fine-tuning.

Automated summary

The realization of global symmetries in quantum-gravity-matter-systems has significant phenomenological implications. Within an asymptotically safe context, it is suggested that discrete global symmetries of the form Z(n), n > 4, cannot be realized in a near-perturbative regime, while an effective-field-theory approach to quantum gravity may feature such symmetries and provide a mechanism for generating mass hierarchies in the infrared without additional fine-tuning.