A unified approach to holomorphic anomaly equations and quantum spectral curves
Abstract
We present a unified approach to holomorphic anomaly equations and some wellknown quantum spectral curves. We develop a formalism of abstract quantum field theory based on the diagrammatics of the DeligneMumford moduli spaces {\overline{M}}_{g,n} and derive a quadratic recursion relation for the abstract free energies in terms of the edgecutting 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.
 Publication:

Journal of High Energy Physics
 Pub Date:
 April 2019
 DOI:
 10.1007/JHEP04(2019)135
 arXiv:
 arXiv:1808.05343
 Bibcode:
 2019JHEP...04..135W
 Keywords:

 String Duality;
 String theory and cosmic strings;
 Topological Strings;
 Mathematical Physics;
 Mathematics  Symplectic Geometry
 EPrint:
 A section is added