论文标题
CFT的阳性，低扭曲优势和CSDR
Positivity, low twist dominance and CSDR for CFTs
论文作者
论文摘要
我们考虑了与相同的标量运算符相关的CFT四点相关的交叉对称分散关系（CSDR），该关联显然是在交叉比例$ u，v $互换下的对称性。该表示形式与CSDR具有多个用于量子场理论的特征。它可以研究相关函数围绕$ u = v = 1/4 $的扩展，该函数用于数值共形性引导程序。我们使用$φ_{1,2} $运算符在2D最小模型中作为测试床的四个点相关函数阐明了色散表示的几个显着特征。当外部标量操作员的尺寸（$δ_σ$）小于$ \ frac {1} {2} $时，CSDR仅从全球主要主要操作员的单个塔中获得贡献，第二座塔被投影。我们发现存在一个低扭曲优势（LTD）的概念，该概念是$Δ_σ$的函数，在2D ISING模型以及非单身Yang-Lee模型附近最大化。 CSDR和LTD进一步解释了围绕交叉对称点的相关函数的泰勒膨胀系数的阳性，并导致对这些系数的特定比率的普遍预测。这些结果以$ 4-ε$尺寸为Epsilon扩展。我们还对几何函数理论思想进行初步研究，即Bieberbach-Rogosinski界限。
We consider a crossing symmetric dispersion relation (CSDR) for CFT four point correlation with identical scalar operators, which is manifestly symmetric under the cross-ratios $u,v$ interchange. This representation has several features in common with the CSDR for quantum field theories. It enables a study of the expansion of the correlation function around $u=v=1/4$, which is used in the numerical conformal bootstrap program. We elucidate several remarkable features of the dispersive representation using the four point correlation function of $Φ_{1,2}$ operators in 2d minimal models as a test-bed. When the dimension of the external scalar operator ($Δ_σ$) is less than $\frac{1}{2}$, the CSDR gets contribution from only a single tower of global primary operators with the second tower being projected out. We find that there is a notion of low twist dominance (LTD) which, as a function of $Δ_σ$, is maximized near the 2d Ising model as well as the non-unitary Yang-Lee model. The CSDR and LTD further explain positivity of the Taylor expansion coefficients of the correlation function around the crossing symmetric point and lead to universal predictions for specific ratios of these coefficients. These results carry over to the epsilon expansion in $4-ε$ dimensions. We also conduct a preliminary investigation of geometric function theory ideas, namely the Bieberbach-Rogosinski bounds.
