Eynard-Orantin Topological Recursion, Moduli-Space Virasoro Constraints, and Semisimple CohFTs

@misc{xiong2026eynardorantin,
  title = {{Eynard-Orantin Topological Recursion, Moduli-Space Virasoro Constraints, and Semisimple CohFTs}},
  author = {Dingkang Xiong and Jian Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.24980},
  eprint = {2610.24980},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.24980},
}

TY  - UNPB
TI  - Eynard-Orantin Topological Recursion, Moduli-Space Virasoro Constraints, and Semisimple CohFTs
AU  - Dingkang Xiong
AU  - Jian Zhou
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2610.24980
UR  - https://arxiv.org/abs/2610.24980
AB  - We use Virasoro constraints to prove Eynard's intersection-number formula for Eynard-Orantin topological recursion with several simple ramification points. The key construction couples the higher Weil-Petersson partition functions associated with the individual ramification points through a quadratic differential operator determined by the Bergman kernel. We identify this operator with the quadratic part of Givental's quantized R-matrix, thereby obtaining a Virasoro-theoretic proof of the DOSS identification of topological recursion with Givental's formula for semisimple cohomological field theories. Furthermore, while the DOSS identification fixes the distinguished y-function, we keep the Bergman kernel/R-matrix fixed and allow y to vary, showing that this amounts to shifting the evaluation point of the corresponding ancestor potential.
ER  -