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Reduction technique for expanding the Feynman diagrams in AdS2

  • V. S. Khiteev
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Abstract

We formulate the reduction technique for expanding the n-point AdS Feynman diagrams in two dimensions into the Wilson line networks. The technique applies to any n-point tree diagram, expressing it as several series of the matrix elements of Wilson line network operators, and employs the Wilson network expansions of the (n−1)-point AdS Feynman diagrams, which can in turn be obtained using the same technique. Consequently, the complexity of this technique does not increase with n, provided that the expansions of the (n−1)-point diagrams are known. To demonstrate the reduction technique, we apply it to all topologically distinct five-point AdS Feynman tree diagrams. The resulting expansions near the conformal boundary reproduce the known decompositions of the corresponding five-point Witten diagrams into conformal blocks.

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Cite

BibTeXRIS
BibTeX
@misc{khiteev2026reduction,
  title = {{Reduction technique for expanding the Feynman diagrams in AdS$_2$}},
  author = {V. S. Khiteev},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.29306},
  eprint = {2609.29306},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.29306},
}
RIS
TY  - UNPB
TI  - Reduction technique for expanding the Feynman diagrams in AdS_2
AU  - V. S. Khiteev
PY  - 2026
DA  - 2026/09/26
PB  - arXiv
DO  - 10.48550/arxiv.2609.29306
UR  - https://arxiv.org/abs/2609.29306
AB  - We formulate the reduction technique for expanding the n-point AdS Feynman diagrams in two dimensions into the Wilson line networks. The technique applies to any n-point tree diagram, expressing it as several series of the matrix elements of Wilson line network operators, and employs the Wilson network expansions of the (n−1)-point AdS Feynman diagrams, which can in turn be obtained using the same technique. Consequently, the complexity of this technique does not increase with n, provided that the expansions of the (n−1)-point diagrams are known. To demonstrate the reduction technique, we apply it to all topologically distinct five-point AdS Feynman tree diagrams. The resulting expansions near the conformal boundary reproduce the known decompositions of the corresponding five-point Witten diagrams into conformal blocks.
ER  -