Do complex fixed points explain the pseudocritical drift at deconfined transitions?
In plain words
One explanation of the slow drift is that the true critical point has moved slightly into complex values of the couplings, so the system behaves almost critically over a very large range of lengths. This idea predicts specific scaling dimensions that can be computed and checked.
Precise statement
For the $SO(5)$-symmetric Neel-VBS problem (NCCP1 or QED3 with $N_f = 2$ description), test the scenario of two nearly merged complex conformal fixed points: compute the real and imaginary parts of the scaling dimensions of the leading singlet and of the $SO(5)$ vector and tensor operators, and the predicted length $\xi*$ beyond which first-order behavior appears. An answer gives these numbers and a quantitative comparison with lattice drifts of $\nu$ and $\eta$.
What would settle it
Fuzzy-sphere or non-Hermitian lattice computations of complex scaling dimensions that quantitatively reproduce the lattice drifts of $\nu$ and $\eta$ and the observed first-order length scale.
Status in the literature
Fuzzy-sphere studies since 2023 report approximate conformal symmetry and operator spectra consistent with nearly real complex fixed points; a quantitative match to the lattice drifts is lacking.