Universality class of the non-Abelian learnability transition

Establish whether the spin-sharpening transition of the SU(2)-symmetric monitored circuit belongs to the universality class of the generic measurement-induced transition governed by ordering of the replica-pairing field, tensored with the spectator diffusive background sector.

Background

The large-loop-fugacity analysis finds that the replica-pairing sector is coupled to a gapless diffusive background whose induced interaction is short-ranged in the renormalization-group sense. On this basis, the paper conjectures that the transition has the same universality class as the generic measurement-induced transition without a global symmetry, together with a spectator critical spin-wave sector. This remains a conjecture because the analysis is controlled only at leading order in the large-loop-fugacity expansion and assumes continuation to the physical SU(2) value.

References

We thus conjecture that the transition is in the universality class of the generic measurement-induced transition of monitored circuits without a global symmetry (governed by the ordering of the $S_Q$ pairing field), tensored with the spectator critical background sector.

— Statistical Mechanics of Non-Abelian Learnability Transitions  (2608.19325 - Ma et al., 19 Aug 2026) in Background sector and induced interaction; Section 3, “Universality class of the spin-sharpening transition”