Integrability of the holomorphic anomaly equations

Details Integrability of the holomorphic anomaly equations Integrability of the holomorphic anomaly equations

2008-09-10

arxiv.org/abs/0809.1674v2

JHEP 0810:097,2008

Physics

High Energy Physics

High Energy Physics - Theory

47 pages, 3 figures; v2: fixed typos, added journal-ref

Scientific paper

10.1088/1126-6708/2008/10/097

We show that modularity and the gap condition make the holomorphic anomaly equation completely integrable for non-compact Calabi-Yau manifolds. This leads to a very efficient formalism to solve the topological string on these geometries in terms of almost holomorphic modular forms. The formalism provides in particular holomorphic expansions everywhere in moduli space including large radius points, the conifold loci, Seiberg-Witten points and the orbifold points. It can be also viewed as a very efficient method to solve higher genus closed string amplitudes in the $\frac{1}{N^2}$ expansion of matrix models with more then one cut.

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