A bstract In recent papers 1, 2, a new method to cross the natural boundary has been proposed, and applied to Mordell-Borel integrals arising in the study of Chern-Simons theory, based on decompositions into resurgent cyclic orbits. Resurgent analysis on the Stokes line leads to a unique transseries decomposition in terms of unary false theta functions, which can be continued across the natural boundary to produce dual q -series whose integer-valued coefficients enumerate BPS states. This constitutes a deeper new manifestation of resurgence in quantum field theoretic path integrals. In this paper we show that the algebraic structure of the resurgent cyclic orbits, combined with just the leading term of the q -series, completely determines the large order rate of growth of the dual q -series coefficients. The essential exponent of this asymptotic growth has a Cardy-like interpretation 12 of an effective central charge in a 3 dimensional quantum field theory with N=2 N = 2 supersymmetry related to the Chern-Simons theory through the 3 d -3 d correspondence.
Adams et al. (Thu,) studied this question.