Coherent state excitations and string-added coherent states in gauge-gravity correspondence

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.