ceff from Resurgence at the Stokes Line

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 [10] of an effective central charge in a 3 dimensional quantum field theory with N=2 supersymmetry related to the Chern-Simons theory through the $3d$-$3d$ correspondence.