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A Unified Approach to Holomorphic Anomaly Equations and Quantum Spectral Curves
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
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.Comment: A section is adde
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