Abstract: An idea to formulate string theory or M-theory by a gauge theory attracts theorists and has been extensively studied. The gauge theory should be lower dimensional so that a geometry in string or M-theory, which has higher dimensions, must emerge from it. Especially, M5-brane realisation in matrix models has been a long-standing mystery. In this talk, we consider a one-dimensional matrix model, called the BMN matrix model, which is considered as a non-perturbative formulation of M-theory. In the BMN matrix model, there are some evidences that spherical M2- and M5-branes correspond to vacua of the matrix model. While it is easy to understand realisation of M2-brane geometries because the vacua form fuzzy 2-spheres, it requires non-perturbative computation in a strongly coupled regime to obtain realisation of M5-brane geometries. We solve this notorious problem by using the supersymmetric localisation method and see how the M-brane geometries are successfully obtained. Intriguingly, this result gives us a consistent picture of how the gravity-side spacetime in the gauge/gravity correspondence emerges from the matrix model.

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