We explore the emergence of locality and geometry in string theories from the perspective of gauge theories using gauge / gravity duality.

First, we explicitly construct open strings stretched between giant gravitons in N=4 SYM. We find that these strings satisfy a relativistic dispersion relation up to three-loop order and conjecture that this should hold to all loop orders. We find the explicit dual solution to the string sigma model and find exact agreement with the geometric nature of the SYM operator and dispersion relation. Using these open strings as probes, we explore the local field theory on the worldvolume of the giant gravitons.

Second, we use classical configurations in holographic matrix models to understand the emergence of geometry from matrix coordinates. We construct an effective Hamiltonian for a probe brane that observes the geometry in a background matrix configuration from which we can construct membranes embedded in three dimensional space. Adding angular momentum to these configurations we are able to observe continuous topology changes. We also study the classical evolution of holographic matrix models to generate a microcanonical ensemble of configurations and study their thermal and chaotic behavior. We argue that these thermal configurations are dual to black holes.