Description
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. This suggests that
there should be a phase transition in the gauge theory and that the
geometry would appear as its temperature decreases. In this talk, we
focus on the BMN matrix model, which is considered as a
non-perturbative formulation of M-theory on the pp-wave geometry and
also conjectured to have a gauge/gravity duality, which relates each
vacuum on the gauge theory side to a bubbling geometry in the type IIA
supergravity. Our preliminary results of Monte Carlo simulations show
two phase transitions and one of them looks related with emergent
geometry.
