Determine whether the bosonic and fermionic DQCP descriptions are dual

Determine whether the non-compact CP$^{1}$ theory with fractionalized bosonic spinons coupled to an emergent U(1) gauge field and the fermionic five-component SO(5)-symmetric description provide dual descriptions of the same antiferromagnetic–valence-bond-solid deconfined quantum critical point.

Background

The paper discusses two complementary descriptions of the direct antiferromagnetic (AFM)–valence-bond-solid (VBS) transition. In the bosonic formulation, the transition is described by a non-compact CP1^{1} theory involving fractionalized bosonic spinons coupled to an emergent U(1) gauge field. In the fermionic formulation, the three AFM and two VBS order-parameter components form a five-component vector associated with an emergent SO(5) symmetry.

The equivalence of these formulations is presented as a conjecture rather than an established result. Establishing the proposed duality would clarify whether the bosonic and fermionic theories describe the same critical fixed point and would strengthen the theoretical interpretation of the observed AFM–VBS transition as a deconfined quantum critical point.

References

These bosonic and fermionic formulations are conjectured to provide dual descriptions of the same critical point, i.e. the DQCP.

— Unconstrained compact lattice QED$_{2+1}$ coupled to phonons: Gauss sectors, orthogonal semimetal, and deconfined criticality  (2609.20502 - Inácio et al., 17 Sep 2026) in Section 4.4, “AFM-VBS transition”