In gauge/gravity duality, the information regarding the gravitational geometry (e.g., black hole and smooth exterior geometry) has to be encoded in gauge theory. Clearly, the color degrees of freedom (matrix degrees of freedom) should play the key role, because the duality can hold even when the gauge theory side is a matrix model. In this talk, I will suggest a simple way of encoding the geometry to matrices, along the line of Witten's work on the effective action of D-branes and strings, and the Matrix Theory conjecture by Banks, Fischler, Shenker and Susskind. Roughly speaking, eigenvalues of matrices can be identified with the location of the D-brane probe or extended objects such as black hole. 



Actually there is a famous argument against such simple interpretation advocated by Polchinski in 1998. His argument used generic properties of large-N gauge theory to show that the ground-state wave function delocalizes at large N, leading to a conflict with the locality in the bulk geometry. We show that this argument is not correct: the ground-state wave function does not delocalize, and there is no conflict with the locality of the bulk geometry. In order to understand how the old argument fails, recently-discovered connection between color confinement and Bose-Einstein condensation is useful. This confinement-BEC connection has a striking consequence: in the SU(N) gauge theory, there is a partially-deconfined phase in which an SU(M)-subgroup is deconfined. Partial deconfinement, combined with the "eigenvalue = location" picture, provides us with a natural scenario to realize the idea in BFSS Matrix Theory conjecture --- extended objects, such as black hole, are realized as bound states of D-branes and strings, that look like non-commutative blocks in big matrices --- in the Maldacena-type gauge/gravity duality. In the large-N limit, various many-body states can be realized by considering block-diagonal matrix configurations, similarly to the BFSS proposal. Therefore, the large-N limit of gauge theory can be interpreted as the second quantization of the gravity side. 



If time permits, we will discuss how we might be able to check this proposal quantitatively, via classical or quantum simulations.