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

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.

30 pages, embedded figures

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• Non-Abelian Binding Energies from the Lightcone Bootstrap
• (2,2) Superconformal Bootstrap in Two Dimensions
• Evidence for a Non-Supersymmetric 5d CFT from Deformations of 5d $SU(2)$ SYM
• Bootstrap experiments on higher dimensional CFTs
• N=4 Superconformal Bootstrap of the K3 CFT
• Inverse Bootstrapping Conformal Field Theories
• New method for the conformal bootstrap with OPE truncations
• ${\varphi }^3$ theory with $F_4$ flavor symmetry in $6-2\epsilon$ dimensions: 3-loop renormalization and conformal bootstrap
• Massless and Massive Higher Spins from Anti-de Sitter Space Waveguide
• The Epsilon-Expansion from Conformal Field Theory
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• Universal Bounds on Operator Dimensions in General 2D Conformal Field Theories
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