Long-Range Vector Models at Large N

We calculate various CFT data for the $O(N)$ vector model with the long-range interaction, working at the next-to-leading order in the $1\mathrm{/}N$ expansion. Our results provide additional evidence for the existence of conformal symmetry at the long-range fixed point, as well as the continuity of the CFT data at the long-range to short-range crossover point $s_{\star }$ of the exponent parameter $s$. We also develop the $N>1$ generalization of the recently proposed IR duality between the long-range and the deformed short-range models, providing further evidence for its non-perturbative validity in the entire region $d\mathrm{/}2<s<s_{\star }$.