  NASA's Kepler mission has discovered thousands of planetary systems, ~20% of
which are found to host multiple transiting planets. This relative paucity
(compared to the high fraction of single transiting systems) is postulated to
result from a distinction in the architecture between multi-transiting systems
and those hosting a single transiting planet: a phenomenon usually referred to
as the Kepler dichotomy. In this paper, we investigate the hypothesis that
external giant planets are the main cause behind the over-abundance of single-
relative to multi-transiting systems, which would be signaled by higher
metallicities in the former sample. To this end, we perform a statistical
analysis on the stellar metallicity distribution with respect to planet
multiplicity in the Kepler data. We perform our analysis on a variety of
samples taken from a population of 1166 Kepler main sequence planetary hosts,
using precisely determined metallicities from the California-Kepler survey and
Swift et al. (2015). Contrary to some predictions, we do not find a significant
difference between the stellar metallicities of the single- and
multiple-transiting planet systems. However, we do find a 55% upper bound for
systems with a single non-giant planet that could also host a hidden giant
planet, based on metallicity considerations. While the presence of external
giant planets might be one factor behind the Kepler dichotomy, our results also
favor alternative explanations. We suggest that additional radial velocity and
direct imaging measurements are necessary to constrain the presence of gas
giants in systems with a single transiting planet.
