标题： 重CFT关联函数的矩和鞍点 显示英文标题

标题： Moments and saddles of heavy CFT correlators

摘要： 我们研究了共形四点关联函数中相同标量的算子乘积展开（OPE），将其视为Stieltjes矩问题，并使用Riemann-Liouville类型的分数微分算子将关联函数转换为经典矩生成函数。我们利用交叉对称性，在大外部标度维数的“重”极限下，推导出$\Delta$和$J_2 = \ell(\ell+d-2)$中矩之间的主要和次主要关系，并结合单位性约束，得出$\Delta$中矩序列以及$\Delta$和$J_2$之间协方差的双侧界限。达到这些界限的矩序列产生交叉方程的“鞍点”解，我们将其识别为广义自由场（GFF）理论中关联函数的特定极限。这促使我们通过鞍点分析研究重GFF四点关联函数的扰动，并表明OPE中的鞍点来源于由变形高自旋共形块分解所编码的固定长度算子族的贡献。为了应用我们的技术，我们考虑了被体相互作用扰动的四个相同单标量场的全息关联函数，并利用它们的前几个矩，推导出高斯权重插值函数，该函数预测了重极限下相互作用双扭 operator 的OPE系数。我们进一步计算了平面$\mathcal{N} = 4$SYM中1/2 BPS威尔逊线缺陷关联函数中鞍点的树级扰动，对长算子族的变形做出预测。 显示英文摘要

摘要： We study the operator product expansion (OPE) of identical scalars in a conformal four-point correlator as a Stieltjes moment problem, and use Riemann-Liouville type fractional differential operators to transform the correlation function into a classical moment-generating function. We use crossing symmetry to derive leading and subleading relations between moments in $\Delta$ and $J_2 = \ell(\ell+d-2)$ in the ``heavy" limit of large external scaling dimension, and combine them with constraints from unitarity to derive two-sided bounds on moment sequences in $\Delta$ and the covariance between $\Delta$ and $J_2$. The moment sequences which saturate these bounds produce ``saddle point" solutions to the crossing equations which we identify as particular limits of correlators in a generalized free field (GFF) theory. This motivates us to study perturbations of heavy GFF four-point correlators by way of saddle point analysis, and we show that saddles in the OPE arise from contributions of fixed-length operator families encoded by a decomposition into deformed higher-spin conformal blocks. To apply our techniques, we consider holographic correlators of four identical single scalar fields perturbed by a bulk interaction, and use their first few moments to derive Gaussian weight-interpolating functions that predict the OPE coefficients of interacting double-twist operators in the heavy limit. We further compute tree-level perturbations on saddles in 1/2 BPS Wilson line defect correlators in planar $\mathcal{N} = 4$ SYM, making predictions about deformations of families of long operators.