Inversion and Integral Identities in dCFTs

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 $\epsilon$ in the $\epsilon$-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.