Fourier-Like Transforms of Stable Graphs and Holomorphic Anomaly Equations

TL;DR

This paper develops Fourier-like transforms for stable graphs, introduces a duality theory, and derives holomorphic anomaly equations for propagators, advancing the mathematical understanding of graph transformations and their applications in theoretical physics.

Contribution

It presents a novel Fourier-like transform framework for stable graphs and establishes a duality theory, linking graph theory with holomorphic anomaly equations.

Findings

Established a duality theory for stable graphs

Derived holomorphic anomaly equations for general propagators

Provided new mathematical tools for graph transformations

Abstract

In this paper we develop a theory of Fourier-like transforms on the space of stable graphs. In particular, we introduce a duality theory of stable graphs. As an application, we derive the holomorphic anomaly equations for general propagators in the work of Aganagic, Bouchard and Klemm.