Eynard-Orantin Topological Recursion, Moduli-Space Virasoro Constraints, and Semisimple CohFTs
Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Xiong, Dingkang, Zhou, Jian
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G5276749214, G7776816500
OpenAlex ID: W7223014442