Abstract
We use the conformal bootstrap approach to explore 5D CFTs with O(N) global symmetry, which contain N scalars ϕ i transforming as O(N) vector. Specifically, we study multiple four-point correlators of the leading O(N) vector ϕ i 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 (Δ ϕ , Δ σ ) of ϕ i and σ. With reasonable assumptions on the gaps between scaling dimensions of ϕ i (σ) and the next O(N) vector ϕ ′ i (singlet σ ′) scalar, we are able to isolate the scaling dimensions (Δ ϕ , Δ σ ) 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 (Δ ϕ , Δ σ ) 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 Δ σ ′ ≥ 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 N c > 100, below which the interacting O(N) CFTs turn into nonunitary.
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Li, Z., Su, N. Bootstrapping mixed correlators in the five dimensional critical O(N) models. J. High Energ. Phys. 2017, 98 (2017). https://doi.org/10.1007/JHEP04(2017)098
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DOI: https://doi.org/10.1007/JHEP04(2017)098