Perturbative Defect CFT Data in Scalar Models and Consistency Conditions

Abstract

We compute defect CFT data through $O(\epsilon )$ for scalar line defects in the $O(N)$, hypercubic, hypertetrahedral, $O(m)\times O(n)$ biconical, and $MN$ models in $d=4-\epsilon$. The $O(N)$ theory provides a benchmark; the datasets for the other four models are new. For the branches considered, we determine spectra, operator mixing, two- and three-point coefficients in a specified perturbative basis, and four-point functions with identical or paired external operators of integer dimension $n\le 2$ at $\epsilon =0$. We propose a framework for verifying perturbative defect CFT data by combining crossing symmetry, OPE reconstruction, and the applicable broken-symmetry integral identities. We also identify a new universal defect-direction sector whose one-loop data follow from the defect fixed-point equation. All applicable conditions are satisfied at the perturbative orders considered. The model data are collected in the supplemental notebook, defect_cft_data.nb.

arXiv comment31 pages. Supplemental Mathematica notebook included