Perturbative Defect CFT Data in Scalar Models and Consistency Conditions
Abstract
We compute defect CFT data through O(ε) for scalar line defects in the O(N), hypercubic, hypertetrahedral, O(m)× O(n) biconical, and MN models in d=4−ε. 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≤2 at ε=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.
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BibTeX
@misc{kong2026perturbative,
title = {{Perturbative Defect CFT Data in Scalar Models and Consistency Conditions}},
author = {Ziwen Kong},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22591},
eprint = {2610.22591},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22591},
note = {CC0},
}
RIS
TY - UNPB
TI - Perturbative Defect CFT Data in Scalar Models and Consistency Conditions
AU - Ziwen Kong
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.22591
UR - https://arxiv.org/abs/2610.22591
AB - We compute defect CFT data through O(ε) for scalar line defects in the O(N), hypercubic, hypertetrahedral, O(m)× O(n) biconical, and MN models in d=4−ε. 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≤2 at ε=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.
ER -