Non-Wilson-Fisher kinks of O(N) numerical bootstrap. From the deconfined phase transition to a putative new family of CFTs

It is well established that the O(N) Wilson-Fisher (WF) CFT sits at a kink of the numerical bounds from bootstrapping four point function of O(N) vector. Moving away from the WF kinks, there indeed exists another family of kinks (dubbed non-WF kinks) on the curve of O(N) numerical bounds. Different from the O(N) WF kinks that exist for arbitary N in 2 < d < 4 dimensions, the non-WF kinks exist in arbitrary dimensions but only for a large enough N > N${}_c$(d) in a given dimension d. In this paper we have achieved a thorough understanding for few special cases of these non-WF kinks. The first case is the O(4) bootstrap in 2d, where the non-WF kink turns out to be the SU(2)${}_1$ Wess-Zumino-Witten (WZW) model, and all the SU(2)${}_{k>2}$ WZW models saturate the numerical bound on the left side of the kink. This is a mirror version of the Z${}_2$ bootstrap, where the 2d Ising CFT sits at a kink while all the other minimal models saturating the bound on the right. We further carry out dimensional continuation of the 2d SU(2)${}_1$ kink towards the 3d SO(5) deconfined phase transition. We find the kink disappears at around d = 2.7 dimensions indicating the SO(5) deconfined phase transition is weakly first order. The second interesting observation is, the O(2) bootstrap bound does not show any kink in 2d (N${}_c$=2), but is surprisingly saturated by the 2d free boson CFT (also called Luttinger liquid) all the way on the numerical curve. The last case is the N = $\infty$ limit, where the non-WF kink sits at (Δ${}_{\varphi }$,Δ${}_T$)=(d - 1,2d) in d dimensions. We manage to write down its analytical four point function in arbitrary dimensions, which equals to the subtraction of correlation functions of a free fermion theory and generalized free theory. An important feature of this solution is the existence of a full tower of conserved higher spin current. We speculate that a new family of CFTs will emerge at non-WF kinks for finite N, in a similar fashion as O(N) WF CFTs originating from free boson at N = $\infty$.