Abstract The O(N) Non-Linear Sigma Model (NLSM) in d = 2 + ε has long been conjectured to describe the same conformal field theory (CFT) as the Wilson-Fisher (WF) O(N) fixed point obtained from the λ(φ2)2 model in d = 4 − ε. In this work, we put this conjecture into question, building on the recent observation 1 that the NLSM CFT possesses a protected operator with dimension N − 1, which is instead absent in the WF O(N) CFT. We investigate the possibility of lifting this operator via multiplet recombination - the only known mechanism that could resolve this mismatch while preserving a connection between the two theories. We also explore an alternative scenario in which the NLSM O(N) fixed point in d = 2 + ε is not continuously connected to the WF O(N) CFT, and instead corresponds to a different universality class. For N = 3, this could be related to the hedgehog-suppressed critical point, which describes the Néel-VBS phase transition in 3D.
Cesare et al. (Mon,) studied this question.