Who told you magnetization is a vector in $4-\epsilon$ dimensions?

Abstract

But if you treat it as a two-form, you get three nontrivial renormalization group fixed points! Which becomes the Heisenberg fixed point in three dimensions? Motivated by this question, we study the conformal bootstrap constraint in the $O(d)$ anti-symmetric matrix model in $d$ dimensions, varying $d$ as a continuous parameter. Besides the one that is naturally connected to the Heisenberg fixed point in three dimensions, we find "evanescent" kinks whose origin is yet to be identified. We also bootstrap $O(4), O(5), O(6)$ anti-symmetric matrix model in $d=3$, aiming at physical applications.