  We study numerically the saddle point structure of two-dimensional (2D)
lattice gauge theory, represented by the Gross-Witten-Wadia unitary matrix
model. The saddle points are in general complex-valued, even though the
original integration variables and action are real. We confirm the
trans-series/instanton gas structure in the weak-coupling phase, and identify a
new complex-saddle interpretation of non-perturbative effects in the
strong-coupling phase. In both phases, eigenvalue tunneling refers to
eigenvalues moving off the real interval, into the complex plane, and the
weak-to-strong coupling phase transition is driven by saddle condensation.
