2025/05/27 by De Cesare, Fabiana, Rychkov, Slava
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Statistical Mechanics (cond-mat.stat-mech) #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.2505.21611
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 [Jones (2024)] 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.