缺陷共形场论（dCFTs）中的反演与积分恒等式
Inversion and Integral Identities in dCFTs
AI总结：
本研究利用已有恒等式推导缺陷共形场论四点函数的反演方法，建立递推关系以带线缺陷O(N)模型验证，高效计算CFT数据，比传统方法更快捷，还探索通用假设并预测OPE系数修正。
摘要：
本研究推导了arXiv:hep-th/0602028中恒等式的一项应用，用于反演缺陷共形场论（dCFTs）中的四点函数。为此建立了递推关系，并以带线缺陷的O(N)模型作为该应用的测试平台。具体而言，通过反演倾斜和位移四点函数计算了共形场论（CFT）数据。该递推关系可高效计算ε展开中ε阶的超几何函数，从而实现四点函数的反演并推导CFT数据。所提出的反演方法相比采用arXiv:hep-ph/0507094v2、arXiv:0708.2443v2的传统方法是更快捷的替代方案。研究还探索了一种通用假设方法，评估了该算法的约束性，最后考察了对arXiv:2203.17157v2的积分恒等式约束的影响，预测了对算子乘积展开（OPE）系数的修正。
英文摘要：
This work derives an application from the identities of arXiv:hep-th/0602028 in order to invert four point functions in defect conformal field theories. For this, a recursion relation is established and the O(N) model with a line defect is considered as a testing ground of this application. Specifically, the CFT data are calculated from inversion of tilt and displacement four point functions. The recursion relation enables efficient computation of hypergeometrics at order $ε$ in the $ε$-expansion, leading to the inversion of four point functions and the derivation of CFT data. The inversion method presented offers a faster alternative to traditional approaches using arXiv:hep-ph/0507094v2, arXiv:0708.2443v2. The study also explores a general ansatz approach, assessing the algorithm's restrictiveness, and concludes by examining implications for the integral identity constraint of arXiv:2203.17157v2, predicting corrections to OPE coefficients.
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