Conformal Bootstrap Approach to O(N) Fixed Points in Five Dimensions

TL;DR

This paper demonstrates the existence of O(N) conformal fixed points in five dimensions using a novel two-gap conformal bootstrap method, aligning with large-N predictions and extending to N=1.

Contribution

It introduces a new two-gap bootstrap approach to locate nontrivial fixed points in five-dimensional O(N) models, revealing their position at the tips of the allowed region.

Findings

Nontrivial fixed points found at tips of the allowed region.

Scaling dimensions match large-N expansion predictions.

Fixed points likely exist for all N down to 1.

Abstract

Whether O(N)-invariant conformal field theory exists in five dimensions with its implication to higher-spin holography was much debated. We find an affirmative result on this question by utilizing conformal bootstrap approach. In solving for the crossing symmetry condition, we propose a new approach based on specification for the low-lying spectrum distribution. We find the traditional one-gap bootstrapping is not suited since the nontrivial fixed point expected from large-N expansion sits at deep interior (not at boundary or kink) of allowed solution region. We propose two-gap bootstrapping that specifies scaling dimension of two lowest scalar operators. The approach carves out vast region of lower scaling dimensions and universally features two tips. We find that the sought-for nontrivial fixed point now sits at one of the tips, while the Gaussian fixed point sits at the other tip. The scaling dimensions of scalar operators fit well with expectation based on large-N expansion. We also find indication that the fixed point persist for lower values of N all the way down to N=1. This suggests that interacting unitary conformal field theory exists in five dimensions for all nonzero N.