  Nearby massive compact elliptical galaxies (MCEGs) are strong candidates for
relic galaxies (i.e. local analogs of red nuggets at high redshifts). It is
expected that the globular cluster (GC) systems of relic galaxies are dominated
by red (metal-rich) GCs. NGC 1277 is known as a unique example of such a galaxy
in the previous study. In this study, we search for GCs in 12 nearby MCEGs at
distances of $\lesssim 100$ Mpc from the Hubble Space Telescope/Wide Field
Camera 3 F814W($I_{814}$)/F160W($H_{160}$) archival images. We find that most
of these MCEGs host a rich population of GCs with a color range of
$0.0<(I_{814}-H_{160})_0<1.1$. The fractions of their red GCs range from
$f_{RGC} =0.2$ to 0.7 with a mean of $f_{RGC} =0.48\pm0.14$. We divide the MCEG
sample into two groups: one in clusters and the other in groups/fields. The
mean red GC fraction of the cluster MCEGs is $0.60\pm0.06$, which is 0.2 larger
than the value of the group/field MCEGs, $0.40\pm0.10$. The value for the
cluster MCEGs is $\sim$0.3 larger than the mean value of giant early-type
galaxies with similar stellar mass in the Virgo cluster ($f_{RGC}
=0.33\pm0.13$). Our results show that most of the MCEGs in our sample are
indeed relic galaxies. This further implies that a majority of the red GCs in
MCEGs are formed early in massive galaxies and that most MCEGs in the local
universe have rarely undergone mergers after they became red nuggets about 10
Gyr ago.
