Extension of the effective no-global-symmetries mechanism beyond shift symmetry

Ascertain whether an analogous mechanism to the shift-symmetry case—where Asymptotic Safety can effectively violate the symmetry at high energies in scattering amplitudes while preserving modified Ward identities along the renormalisation group flow and restoring symmetry in the infrared—can be realised for other global symmetries within Asymptotic Safety.

Background

The authors present a scenario in which, if physical Asymptotic Safety is realised at the level of scattering amplitudes, shift symmetry can be effectively broken at high energies in amplitudes while remaining unbroken along the RG flow and being restored at low energies. This would align with the no-global-symmetries conjecture without relying on black-hole arguments.

They explicitly note uncertainty about whether such a mechanism generalises to other global symmetries, highlighting an open direction for investigation in Asymptotic Safety.

References

It is however unclear whether a similar mechanism could be realised for other global symmetries.

— Asymptotically (un)safe scattering amplitudes from scratch: a deep dive into the IR jungle  (2602.21285 - Knorr, 24 Feb 2026) in Section 4, '(No) Global symmetries in Asymptotic Safety?'