A Unified Approach to Holomorphic Anomaly Equations and Quantum Spectral Curves

Abstract

We present a unified approach to holomorphic anomaly equations and some well-known quantum spectral curves. We develop a formalism of abstract quantum field theory based on the diagrammatics of the Deligne-Mumford moduli spaces ${\overline{\mathcal{M}}}_{g,n}$ and derive a quadratic recursion relation for the abstract free energies in terms of the edge-cutting operators. This abstract quantum field theory can be realized by various choices of a sequence of holomorphic functions or formal power series and suitable propagators, and the realized quantum field theory can be represented by formal Gaussian integrals. Various applications are given.

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Cited by in corpus (5)

• Fat and Thin Emergent Geometries of Hermitian One-Matrix Models
• Orbifold Euler Characteristics of ${\overline{\mathcal{M}}}_{g,n}$
• A formalism of abstract quantum field theory of summation of fat graphs
• Fourier-Like Transforms of Stable Graphs and Holomorphic Anomaly Equations
• Topological 1D Gravity, KP Hierarchy, and Orbifold Euler Characteristics of ${\overline{\mathcal{M}}}_{g,n}$