Abstract In 1, we revisited the d = 2 + ε expansion in the O(N) Non-Linear Sigma Model (NLSM), emphasizing the existence of a protected operator which is a closed form with N − 1 indices. The scaling dimension of this operator stays exactly equal to N − 1, independently of ε. Its existence is problematic for the identification of the NLSM fixed point in d = 2 + ε with the Wilson-Fisher fixed point family obtained by analytically continuing from near d = 4, which does not possess such a protected operator. Multiplet recombination is one scenario discussed in 1, which could allow to connect the two families continuously (although not analytically). In this scenario, the protected dimension is lifted at some critical value of ε, thanks to the short conformal multiplet of scaling dimension N − 1 eating a long conformal multiplet of higher scaling dimension. In this followup work, we assess this scenario for the cases N = 3 and N = 4. We identify the lowest candidates for the long multiplet which could be eaten, and compute their one-loop anomalous dimensions. We find that at one loop, scaling dimensions of these candidates grow with ε, while it should decrease down to N for the recombination to occur. We conclude that multiplet recombination is unlikely.
Cesare et al. (Wed,) studied this question.