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符乘积展开（OPE）作为一个斯蒂尔吉斯矩问题，并利用黎曼-刘维尔类型的分数阶微分算子从关联函数生成经典矩。 我们在大外部标度维度的“重极限”下，利用交叉对称性推导出 $\Delta$ 和 $J_2 \equiv \ell(\ell+d-2)$ 中矩之间的主导和次主导关系，并结合幺正性的约束条件，推导出 $\Delta$ 中矩序列的双侧界以及 $\Delta$ 和 $J_2$ 之间的协方差。 达到这些界的矩序列产生跨越方程的“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，我们证明OPE中的鞍点来自由高自旋共形块分解编码的固定长度算符族的贡献。 为了应用我们的技术，我们考虑由体相互作用扰动的四个相同单标量场的全息关联函数，并使用它们的前几个矩来推导高斯权重插值函数，以预测重极限下相互作用双扭算符的OPE系数。 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 generate classical moments from the correlation function. We use crossing symmetry to derive leading and subleading relations between moments in $\Delta$ and $J_2 \equiv \ell(\ell+d-2)$ 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 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.