ceff from resurgence at the Stokes line

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 $$ \mathcal{N}=2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:math> supersymmetry related to the Chern-Simons theory through the 3 d -3 d correspondence.