  Over the past few decades, numerous wide (>1000 au) binaries in the Galactic
field and halo have been discovered. Their existence cannot be explained by the
process of star formation or by dynamical interactions in the field, and their
origin has long been a mystery. We explain the origin of these wide binaries by
formation during the dissolution phase of young star clusters: an initially
unbound pair of stars may form a binary when their distance in phase-space is
small. Using N-body simulations, we find that the resulting wide binary
fraction in the semi-major axis range 1000 au - 0.1 pc for individual clusters
is 1-30%, depending on the initial conditions. The existence of numerous wide
binaries in the field is consistent with observational evidence that most
clusters start out with a large degree of substructure. The wide binary
fraction decreases strongly with increasing cluster mass, and the semi-major
axis of the newly formed binaries is determined by the initial cluster size.
The resulting eccentricity distribution is thermal, and the mass ratio
distribution is consistent with gravitationally-focused random pairing. As a
large fraction of the stars form in primordial binaries, we predict that a
large number of the observed 'wide binaries' are in fact triple or quadruple
systems. By integrating over the initial cluster mass distribution, we predict
a binary fraction of a few per cent in the semi-major axis range 1000 au - 0.1
pc in the Galactic field, which is smaller than the observed wide binary
fraction. However, this discrepancy may be solved when we consider a broad
range of cluster morphologies.
