Resurgence in the Universal Structures in B-model Topological String Theory

We propose a systematic analysis of Alim-Yau-Zhou's double scaling limit and Couso-Santamar\'{i}a's large radius limit for the perturbative free energies in B-model topological string theory based on \'Ecalle's Resurgence Theory. Taking advantage of the known resurgent properties of the formal solutions to the Airy equation and of the stability of resurgent series under exponential/logarithm and nonlinear changes of variable, we show how to rigorously derive the non-perturbative information from the perturbative one by means of alien calculus in this context, spelling out the notions of formal integral and Bridge Equation, typical of the resurgent approach to ordinary differential equations. We also discuss the Borel-Laplace summation of the obtained resurgent transseries, including a study of real analyticity based on the connection formulas stemming from the resummation of the Bridge Equation.