Sketches of emergent geometry in the gauge/gravity duality

In this paper three notions of emergent geometry arising from the study of gauge/gravity duals are discussed. The unifying theme behind these notions of emergent geometry is that one can derive properties of the effective action of a probe or excitation around some configuration in gauge theory which can be argued to be localized at a particular position in the gravity dual, and match this description to various degrees of accuracy in the gravity dual. The three examples discussed are giant gravitons in $AdS_5\times S^5$, open strings stretching between these giants and the probe dynamics of a D0 brane in the presence of a thermal matrix configuration of the BFSS matrix model.