  We analyze detailed properties of BPS coherent states and their connection to
gravity. We interpret the group integral coherent state as a path integral over
auxiliary variables coupled to the elementary letters of the theory. The
eigenvalues of coherent state amplitudes can be viewed as collective
coordinates of giant gravitons. Inspired by the above coherent states and by
the integrability, we construct a new type of coherent states in the SL(2)
sectors and their cousin PSU(1,1|2) sectors, analogous to the aforementioned
coherent states. The large spin and small spin limits can be obtained by
varying coherent state amplitudes. We add string words onto the BPS coherent
states, and this gives rise to string-added coherent states. The insertions of
string multi-words can be viewed as operator-insertions in this path integral.
We describe BPS states and near BPS states building upon these coherent states
in gauge-gravity correspondence. For example, string-added coherent states and
their near BPS spectra are analyzed. This approach is particularly convenient
for heavy excited states.
