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. 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 $(\Delta_\phi, \Delta_T)=(d-1, 2d)$ 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 $N=\infty$.

中文翻译：

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$ O（N）$数值引导程序的非Wilson-Fisher纠结：从受限的相变到推定的CFT新家族

众所周知，$ O（N）$ Wilson-Fisher（WF）CFT位于自引导$ O（N）$向量的四点函数的数值边界的转折点。离开WF纽结，确实在$ O（N）$数值范围的曲线上存在另一个纽结家族（称为非WF纽结）。与在$ 2 <d <4 $维度中用于任意$ N $的$ O（N）$ WF纽结不同，非WF纽结存在于任意维度中，但仅用于足够大的$ N> N_c（d）$在给定的尺寸$ d $中。在本文中，我们对这些非WF纽结的一些特殊情况有了透彻的了解。第一种情况是2d中的$ O（4）$引导程序，其中非WF扭结最终是$ SU（2）_1 $ Wess-Zumino-Witten（WZW）模型，以及所有$ SU（2 ）_ {k> 2} $ WZW模型使扭结左侧的数值边界饱和。我们进一步执行2d $ SU（2）_1 $扭结向3d $ SO（5）$限界相变的维连续。我们发现扭结在$ d = 2.7 $维附近消失，表明$ SO（5）$限定相变是弱一阶。第二个有趣的观察结果是，$ O（2）$引导范围在2d（$ N_c = 2 $）中未显示任何扭结，但是令人惊讶地一直被2d自由玻色子CFT（也称为Luttinger液体）饱和数值曲线。最后一种情况是$ N = \ infty $限制，其中非WF纽结位于$ d $维度中的$（\ Delta_ \ phi，\ Delta_T）=（d-1，2d）$。我们设法在任意维度上写下其解析四点函数，这等于减去自由费米子理论和广义自由理论的相关函数。该解决方案的一个重要特征是存在一个完整的守恒高自旋电流塔。我们推测，一个新的CFT家族将以有限的$ N $出现在非WF纽结处，其方式类似于源自自由玻色子的$ O（N）$ WF CFT，其价格为$ N = \ infty $。