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arXiv · 2507.09170

Feynman Graph Integrals on K\"ahler Manifolds

Minghao Wang·Junrong Yan
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Abstract

In this paper, we establish the convergence of Feynman graph integrals on closed real-analytic K\"ahler manifolds and uncover the structural mechanism underlying this convergence. The key insight is that, using Getzler's rescaling technique, the graph integrands extend canonically to the Fulton-MacPherson compactification of configuration spaces as forms with divisorial-type singularities. This allows the Feynman graph integrals to be rigorously defined as Cauchy principal value integrals. As an application, these integrals provide a mathematically rigorous construction of the higher-genus B-model invariants on Calabi-Yau threefolds in the sense of Bershadsky-Cecotti-Ooguri-Vafa (BCOV).

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Minghao Wang, Junrong Yan. 2025-07-12. Feynman Graph Integrals on K\"ahler Manifolds. https://arxiv.org/abs/2507.09170

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