62 Instantons in supersymmetric Yang–Mills theories
Instantons are related to the tunneling amplitudes connecting the vacuum state to itself. In gauge theories at weak coupling this is the main source of the nonperturbative physics shaping the vacuum structure.
In the semiclassical treatment of tunneling transitions, instantons present the extremal trajectories (classical solutions) in imaginary time. Thus, the analytical continuation to imaginary time becomes a necessity. In imaginary time the theory can often be formulated as a field theory in Euclidean space.
However, a Euclidean formulation does not exist in minimal supersymmetric theories ...