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

TL;DR

This paper explores the renormalization group fixed points of an antisymmetric matrix model across dimensions, revealing multiple fixed points and novel features through conformal bootstrap methods.

Contribution

It introduces a bootstrap analysis of the $O(d)$ antisymmetric matrix model in continuous dimensions, uncovering new fixed points and phenomena not previously identified.

Findings

Identification of three nontrivial RG fixed points in the model.

Discovery of 'evanescent' kinks with unknown origins.

Bootstrap results for $O(4), O(5), O(6)$ models in three 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.