The KdV equation governing 2D topological gravity admits a one-parameter transseries; its leading nonperturbative sector reproduces known JT gravity instanton corrections and extends them to multi-instanton order.
On the Genus Expansion in the Topological String Theory
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A systematic formulation of the higher genus expansion in topological string theory is considered. We also develop a simple way of evaluating genus zero correlation functions. At higher genera we derive some interesting formulas for the free energy in the $A_1$ and $A_2$ models. We present some evidence that topological minimal models associated with Lie algebras other than the A-D-E type do not have a consistent higher genus expansion beyond genus one. We also present some new results on the $CP^1$ model at higher genera.
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Non-perturbative effects in JT gravity from KdV equations
The KdV equation governing 2D topological gravity admits a one-parameter transseries; its leading nonperturbative sector reproduces known JT gravity instanton corrections and extends them to multi-instanton order.