  We study a resurgence structure of a quantum field theory with a phase
transition to uncover relations between resurgence and phase transitions. In
particular, we focus on three-dimensional $\mathcal{N}=4$ supersymmetric
quantum electrodynamics (SQED) with multiple hypermultiplets, where a
second-order quantum phase transition has been recently proposed in the
large-flavor limit. We provide interpretations of the phase transition from the
viewpoints of Lefschetz thimbles and resurgence. For this purpose, we study the
Lefschetz thimble structure and properties of the large-flavor expansion for
the partition function obtained by the supersymmetric localization. We show
that the second-order phase transition is understood as a phenomenon where a
Stokes and anti-Stokes phenomenon occurs simultaneously. The order of the phase
transition is determined by how saddles collide at the critical point. In
addition, the phase transition accompanies an infinite number of Stokes
phenomena due to the supersymmetry. These features are appropriately mapped to
the Borel plane structures as the resurgence theory expects. Given the lessons
from the SQED, we provide a more general discussion on the relationship between
the resurgence and phase transitions. In particular, we show how the
information on the phase transition is decoded from the Borel resummation
technique.
