Abstract
Although gauge/gravity dualities have been getting understood with great effort, how the geometries emerge from and embed in gauge theories is still unclear. I show it in the case of the gauge/gravity duality between BMN model and the type IIA supergravity by investigating the exact partition function of the gauge theory. It is revealed that the saddle point equations on the gauge theory side are equivalent to the equations determining the dual geometry on the gravity side, and the ranges of eigenvalue distributions on the gauge theory side actually relates to the typical geometric scales. This thesis is based on [1, 2, 3]
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