Bootstrapping mixed correlators in the five dimensional critical O(N) models

Abstract

We use the conformal bootstrap approach to explore 5D CFTs with O(N) global symmetry, which contain N scalars ϕi transforming as O(N) vector. Specifically, we study multiple four-point correlators of the leading O(N) vector ϕi and the O(N) singlet σ. The crossing symmetry of the four-point functions and the unitarity condition provide nontrivial constraints on the scaling dimensions (Δϕ, Δσ) of ϕi and σ. With reasonable assumptions on the gaps between scaling dimensions of ϕi (σ) and the next O(N) vector ϕi′ (singlet σ′) scalar, we are able to isolate the scaling dimensions (Δϕ, Δσ) in small islands. In particular, for large N = 500, the isolated region is highly consistent with the result obtained from large N expansion. We also study the interacting O(N) CFTs for 1≤N ≤100. Isolated regions on (Δϕ, Δσ) plane are obtained using conformal bootstrap program with lower order of derivatives Λ; however, they disappear after increasing Λ. For N = 100, no solution can be found with Λ = 25 under the assumptions on the scaling dimensions of next O(N) vector {varDelta}_{phi_i^{prime }}ge 5.0 (singlet Δσ′ ≥ 3.3). These islands are expected to be corresponding to interacting but nonunitary O(N) CFTs. Our results suggest a lower bound on the critical value Nc> 100, below which the interacting O(N) CFTs turn into nonunitary.