More on analytic bootstrap for O(N) models

TL;DR

This paper extends the analytical bootstrap approach for O(N) models by including trace and antisymmetric operators, analyzing their impact on anomalous dimensions in the large spin limit, and confirming consistency with epsilon-expansion results.

Contribution

It introduces the effects of additional trace and antisymmetric operators on anomalous dimensions in O(N) models within the analytical bootstrap framework.

Findings

Additional operators influence anomalous dimensions at large spin.

Leading order epsilon-expansion results match the n=0 case.

Holographic setup proposed for N=2 case.

Abstract

This note is an extension of a recent work on the analytical bootstrapping of $O(N)$ models. An additonal feature of the $O(N)$ model is that the OPE contains trace and antisymmetric operators apart from the symmetric-traceless objects appearing in the OPE of the singlet sector. This in addition to the stress tensor $(T_{\mu\nu})$ and the $\phi_i\phi^i$ scalar, we also have other minimal twist operators as the spin-1 current $J_\mu$ and the symmetric-traceless scalar in the case of $O(N)$. We determine the effect of these additional objects on the anomalous dimensions of the corresponding trace, symmetric-traceless and antisymmetric operators in the large spin sector of the $O(N)$ model, in the limit when the spin is much larger than the twist. As an observation, we also verified that the leading order results for the large spin sector from the $\epsilon-$expansion are an exact match with our $n=0$ case. A plausible holographic setup for the special case when $N=2$ is also mentioned which mimics the calculation in the CFT.