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

We use the conformal bootstrap approach to explore 5D CFTs with O(N) global symmetry, which contain N scalars 0, transforming as O(N) vector. Specifically, we study multiple four-point correlators of the leading O(N) vector phi(i), and the O(N) singlet a. The crossing symmetry of the four-point functions and the unitarity condition provide nontrivial constraints on the scaling dimensions (Delta(phi), Delta(sigma)) of phi(i), and a. With reasonable assumptions on the gaps between scaling dimensions of phi(i), (a) and the next O(N) vector phi(i)', (singlet sigma') scalar, we are able to isolate the scaling dimensions (Delta(phi), Delta(sigma)) 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 (A o, Aa) plane are obtained using conformal bootstrap program with lower order of derivatives Lambda; however, they disappear after increasing A. For N = 100, no solution can be found with Lambda = 25 under the assumptions on the scaling dimensions of next O(N) vector Delta phi(i)' >= 5.0 (singlet Delta(sigma)' >= 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.