  Localization methods have recently led to a plethora of new exact results in
supersymmetric gauge theories, as certain observables may be computed in terms
of matrix integrals. These can then be evaluated by making use of standard
large N techniques, or else via perturbative expansions in the gauge coupling.
Either approximation often leads to observables given in terms of asymptotic
series, which need to be properly defined in order to obtain nonperturbative
results. At the same time, resurgent analysis has recently been successfully
applied to several problems, e.g., in quantum, field and string theories,
precisely to overcome this issue and construct nonperturbative answers out of
asymptotic perturbative expansions. The present work uses exact results from
supersymmetric localization to address the resurgent structure of the free
energy and partition function of Chern-Simons and ABJM gauge theories in three
dimensions, and of N=2 supersymmetric Yang-Mills theories in four dimensions.
For each case, the complete structure of Borel singularities is exactly
determined, and the relation of these singularities with the large-order
behavior of (multi-instanton) perturbative expansions is made fully precise.
