# Airy Equation for the Topological String Partition Function in a Scaling Limit

@article{Alim2015AiryEF, title={Airy Equation for the Topological String Partition Function in a Scaling Limit}, author={Murad Alim and Shing-Tung Yau and Jie Zhou}, journal={Letters in Mathematical Physics}, year={2015}, volume={106}, pages={719-729} }

We use the polynomial formulation of the holomorphic anomaly equations governing perturbative topological string theory to derive the free energies in a scaling limit to all orders in perturbation theory for any Calabi–Yau threefold. The partition function in this limit satisfies an Airy differential equation in a rescaled topological string coupling. One of the two solutions of this equation gives the perturbative expansion and the other solution provides geometric hints of the non…

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## References

SHOWING 1-10 OF 22 REFERENCES

### Holomorphicity and modularity in Seiberg-Witten theories with matter

- Physics
- 2009

We calculate the gravitational corrections to the effective action of N=2 SU(2) Seiberg-Witten theory with matter using modularity, the holomorphic anomaly equation and expected behavior at the…

### The Strength of Nonperturbative Effects in String Theory

- Physics
- 1991

We argue that the leading weak coupling nonperturbative effects in closed string theories should be of order exp(— C/κ) where κ 2 is the closed string coupling constant. This is the case in the…

### Polynomial structure of the (open) topological string partition function

- Mathematics
- 2007

In this paper we show that the polynomial structure of the topological string partition function found by Yamaguchi and Yau for the quintic holds for an arbitrary Calabi-Yau manifold with any number…

### String perturbation theory diverges.

- PhysicsPhysical review letters
- 1988

We prove that perturbation theory for the bosonic string diverges for arbitrary values of the coupling constant and is not Borel summable. This divergence is independent of the existence of the…

### Topological string partition functions as polynomials

- Mathematics
- 2004

We investigate the structure of the higher genus topological string amplitudes on the quintic hypersurface. It is shown that the partition functions of the higher genus than one can be expressed as…

### Topological Strings and Integrable Hierarchies

- Mathematics
- 2006

We consider the topological B-model on local Calabi-Yau geometries. We show how one can solve for the amplitudes by using -algebra symmetries which encode the symmetries of holomorphic…

### Analytic Continuation Of Chern-Simons Theory

- Mathematics
- 2010

The title of this article refers to analytic continuation of three-dimensional ChernSimons gauge theory away from integer values of the usual coupling parameter k, to explore questions such as the…

### Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes

- Mathematics
- 1994

We develop techniques to compute higher loop string amplitudes for twistedN=2 theories withĉ=3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in…

### Topological Strings from Quantum Mechanics

- Mathematics
- 2014

We propose a general correspondence which associates a non-perturbative quantum-mechanical operator to a toric Calabi–Yau manifold, and we conjecture an explicit formula for its spectral determinant…

### Lectures on non‐perturbative effects in large N gauge theories, matrix models and strings

- Physics
- 2012

In these lectures I present a review of non‐perturbative instanton effects in quantum theories, with a focus on large N gauge theories and matrix models. I first consider the structure of these…