Inverse KLT kernel of AdS string integrals from the intersection matrix

Abstract

We develop a topological and combinatorial interpretation of the Kawai--Lewellen--Tye (KLT) relations for n-point AdS string-amplitude building blocks, which are disk integrals with multivariable multiple polylogarithm insertions and sphere integrals with their single-valued counterparts. Building on the framework of twisted de Rham theory over a noncommutative ring, we reformulate the problem in terms of associahedral chambers of the moduli space loaded with solutions of the Knizhnik--Zamolodchikov equation. We construct regularized twisted cycles and express their intersection pairings through local monodromies and Drinfeld associators, which control transport between fusion-tree normalizations. Organizing the intersection contributions by common boundary faces yields the intersection matrix, which is identified with the inverse KLT kernel by the twisted period relation. The field-theory limit of the inverse KLT kernel is also given.

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BibTeX RIS

BibTeX

@misc{tao2026inverse,
  title = {{Inverse KLT kernel of AdS string integrals from the intersection matrix}},
  author = {Yi-Xiao Tao and Shijie Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.30862},
  eprint = {2610.30862},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.30862},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Inverse KLT kernel of AdS string integrals from the intersection matrix
AU  - Yi-Xiao Tao
AU  - Shijie Zhang
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.30862
UR  - https://arxiv.org/abs/2610.30862
AB  - We develop a topological and combinatorial interpretation of the Kawai--Lewellen--Tye (KLT) relations for n-point AdS string-amplitude building blocks, which are disk integrals with multivariable multiple polylogarithm insertions and sphere integrals with their single-valued counterparts. Building on the framework of twisted de Rham theory over a noncommutative ring, we reformulate the problem in terms of associahedral chambers of the moduli space loaded with solutions of the Knizhnik--Zamolodchikov equation. We construct regularized twisted cycles and express their intersection pairings through local monodromies and Drinfeld associators, which control transport between fusion-tree normalizations. Organizing the intersection contributions by common boundary faces yields the intersection matrix, which is identified with the inverse KLT kernel by the twisted period relation. The field-theory limit of the inverse KLT kernel is also given.
ER  -

Abstract

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