论文标题
$ o（n）$数字引导程序的非威尔逊 - 法命相关：从脱成相的相变到推定的新的CFT家族
Non-Wilson-Fisher kinks of $O(N)$ numerical bootstrap: from the deconfined phase transition to a putative new family of CFTs
论文作者
论文摘要
众所周知，$ o（n）$ wilson-fisher（wf）CFT位于$ o（n）$ vector的四点函数的数值范围的扭结中。脱离了WF扭结，确实存在着另一个曲线（n）$数值范围的曲线上的另一个扭结（称为non-wf kinks）。与$ o（n）$ wf kinks不同的是，$ n $ in $ 2 <d <4 $尺寸，非WF kinks在任意维度中存在，但仅适用于给定尺寸$ d $的足够大$ n> n_c（d）$。在本文中，我们已经对这些非WF纠结的一些特殊情况有了彻底的了解。第一种情况是2D中的$ o（4）$ bootstrap，其中非WF纠结是$ su（2）_1 $ wess-zumino-witten（WZW）型号，以及所有$ su（2）_ {k> 2} $ wzw型号的数字在kink左侧的数字限制。我们进一步执行了2d $ su（2）_1 $扭结的尺寸延续，以3d $ so（5）$ decontined相过渡。我们发现，扭结消失在$ d = 2.7 $尺寸左右，表明$（5）$ deconindine phase Truntition是弱的一阶。第二个有趣的观察结果是，$ o（2）$ bootstrap绑定并未在2D（$ n_c = 2 $）中显示出任何扭结，但令人惊讶的是，在数值曲线上，2D Free Boson CFT（也称为Luttinger Liquid）饱和。最后一个情况是$ n = \ infty $限制，其中非WF扭结位于$（δ_D，δ_t）=（d-1，2d）$ in $ d $ dimensions中。我们设法在任意维度上写下了其分析四点函数，这等于自由费菲尔米理论和广义自由理论的相关函数的减法。该解决方案的一个重要特征是存在一个完整的保守较高自旋电流的塔。我们推测，新的CFT家族将以有限的$ n $的方式出现在非WF Kinks，其方式与$ O（N）$ WF CFTS相似，该$ wf CFT源自$ n = \ infty $。
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 $(Δ_ϕ, Δ_T)=(d-1, 2d)$ 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 $N=\infty$.
