Abstract

We propose a simple way of encoding the emergent geometry in holography into color degrees of freedom (equivalently, matrix degrees of freedom). Actually, we just claim that a good old picture, “coordinate = matrix eigenvalue”, can work. In the past, it was argued by Polchinski [1] (see also [2]) that this simple picture cannot be used, because the ground-state wave function delocalizes at large N, leading to a conflict with the locality in the bulk geometry. We show this conventional wisdom is wrong; the ground-state wave function does not delocalize, and there is no conflict with the locality of the bulk geometry at all [3]. (In Ref.[1], Polchinski did realize a puzzling feature of his conclusion and suggested that it is necessary to obtain the “low-energy part” of the geometry from matrices. We give a simple and almost trivial way of obtaining such “low-energy part”.) We also analyze the excited states, which are dual to a small black hole. Based on a striking similarity between Bose-Einstein condensation and color confinement at large-$N$ [4], we argue that only a subgroup of the SU(N) gauge group deconfines, and the deconfined sector describes the black hole while the confined sector can be used to probe the exterior geometry [5,3].

[1] Polchinski, “M theory and the light cone”, hep-th/9903165 (Prog.Theor.Phys.Suppl.). [2] Susskind, “Holography in the flat space limit”, hep-th/9901079 (AIP Conf.Proc.). [3] MH, “Bulk geometry in gauge/gravity duality and color degrees of freedom”, 2102.08982 [hep-th] (Phys.Rev.D). [4] MH, Shimada and Wintergerst, “Color confinement and Bose-Einstein condensation”, 2001.10459 [hep-th] (JHEP). [5] MH and Maltz, “A proposal of the gauge theory description of the small Schwarzschild black hole in AdS5​×S5”, 1608.03276 [hep-th] (JHEP).