  The Feynman path integral of ordinary quantum mechanics is complexified and
it is shown that possible integration cycles for this complexified integral are
associated with branes in a two-dimensional A-model. This provides a fairly
direct explanation of the relationship of the A-model to quantum mechanics;
such a relationship has been explored from several points of view in the last
few years. These phenomena have an analog for Chern-Simons gauge theory in
three dimensions: integration cycles in the path integral of this theory can be
derived from N=4 super Yang-Mills theory in four dimensions. Hence, under
certain conditions, a Chern-Simons path integral in three dimensions is
equivalent to an N=4 path integral in four dimensions.
