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arXiv · 1808.05343

A Unified Approach to Holomorphic Anomaly Equations and Quantum Spectral Curves

Zhiyuan Wang·Jian Zhou
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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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Zhiyuan Wang, Jian Zhou. 2019-02-27. A Unified Approach to Holomorphic Anomaly Equations and Quantum Spectral Curves. https://doi.org/10.1007/jhep04(2019)135

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