  Stellar companions can influence the formation and evolution of planetary
systems, but there are currently few observational constraints on the
properties of planet-hosting binary star systems. We search for stellar
companions around 77 transiting hot Jupiter systems to explore the statistical
properties of this population of companions as compared to field stars of
similar spectral type. After correcting for survey incompleteness, we find that
$47\%\pm7\%$ of hot Jupiter systems have stellar companions with semi-major
axes between 50-2000 AU. This is 2.9 times larger than the field star companion
fraction in this separation range, with a significance of $4.4\sigma$. In the
1-50AU range, only $3.9^{+4.5}_{-2.0}\%$ of hot Jupiters host stellar
companions compared to the field star value of $16.4\%\pm0.7\%$, which is a
$2.7\sigma$ difference. We find that the distribution of mass ratios for
stellar companions to hot Jupiter systems peaks at small values and therefore
differs from that of field star binaries which tend to be uniformly distributed
across all mass ratios. We conclude that either wide separation stellar
binaries are more favorable sites for gas giant planet formation at all
separations, or that the presence of stellar companions preferentially causes
the inward migration of gas giant planets that formed farther out in the disk
via dynamical processes such as Kozai-Lidov oscillations. We determine that
less than 20% of hot Jupiters have stellar companions capable of inducing
Kozai-Lidov oscillations assuming initial semi-major axes between 1-5 AU,
implying that the enhanced companion occurrence is likely correlated with
environments where gas giants can form efficiently.
