Multiple stellar populations of globular clusters from homogeneous
  Ca--CN photometry. III. NGC 6752
  We present a multiple stellar population (MSP) study of the globular cluster
(GC) NGC~6752. We show that our new photometric CN index accurately traces the
CN and the nitrogen abundances in cool giants, finding the discrete double red
giant branch (RGB) and asymptotic giant branch (AGB) sequences with number
ratios between the CN-weak and the CN-strong populations of \nrgb\ = 25:75
($\pm$3; RGB) and 79:21 ($\pm$13; AGB). The discrepancy in these number ratios
suggests that a significant fraction of the low-mass \cns\ stars failed to
evolve into the AGB phase. However, unlike previous studies, our results
indicate the presence of an extreme \cns\ AGB population in NGC~6752, which may
require follow-up spectroscopic study. Similar to what is seen for M5, the
evolution of the nitrogen abundance is discrete and discontinuous, while the
evolutions of oxygen and sodium are continuous between the two populations in
NGC~6752, implying that different astrophysical sources are responsible for the
evolutions of these elements. In addition, the helium abundance inferred from
the RGB bump magnitude shows hat the \cns\ population is slightly more
helium-enhanced. Despite the identical cumulative radial distributions between
the two populations, the structure-kinematics coupling can be observed in
individual populations: the \cnw\ population has a spatially elongated shape
with a faster rotation, while the \cns\ population shows weak or no net
rotation, with spatially symmetric shape, raising important question about the
long-term dynamical evolution of the GCs.
