The AdS^2_θ/CFT_1 Correspondence and Noncommutative Geometry III: Phase Structure of the Noncommutative AdS^2_θ x S^2_N
Badis Ydri, Loubna Bouraiou
备注：
This is the third part of a three-parts study in which we attempt a synthesis between the principles of noncommutative geometry and the principles of the gauge/gravity correspondence. Part I:arXiv:2108.13982 [hep-th]. Part II:arXiv:2109.00380 [hep-th]
The near-horizon noncommutative geometry of black holes, given by AdS^2_θ x S^2_N, is discussed and the phase structure of the corresponding Yang-Mills matrix models is presented. The dominant phase transition as the system cools down, i.e. as the gauge coupling constant is decreased is an emergent geometry transition between a geometric noncommutative AdS^2_θ x S^2_N phase (discrete spectrum) and a Yang-Mills matrix phase (continuous spectrum) with no background geometrical structure. We also find a possibility for topology change transitions in which space or time directions grow or decay as the temperature is varied. Indeed, the noncommutative near-horizon geometry AdS^2_θ x S^2_N can evaporate only partially to a fuzzy sphere S^2_N (emergence of time) or to a noncommutative anti-de Sitter spacetime AdS^2_θ (topology change).
In this article we present the construction of noncommutative AdS^2_θ black hole and its four-dimensional Yang-Mills IKKT-type matrix model which includes two competing Myers term one responsible for the condensation of pure AdS^2_θ and the other one responsible for the condensation of the dilaton field. It is argued that the phase diagram of this matrix model features three phases: 1) A gravitational phase (AdS^2_θ black hole), 2) A geometric phase (AdS^2_θ background) and 3) A Yang-Mills phase. The Hawking process is therefore seen as an exotic line of discontinuous transitions between the g…
A consistent QM/NCG duality is put forward as a model for the AdS^2/CFT_1 correspondence. This is a duality/correspondence between 1) the dAFF conformal quantum mechanics (QM) on the boundary (which is only "quasi-conformal" in the sense that there is neither an SO(1,2)-invariant vacuum state nor there are strictly speaking primary operators), and between 2) the noncommutative geometry of AdS^2_θ in the bulk (which is only "quasi-AdS" in the sense of being only asymptotically AdS^2). The Laplacian operators on noncommutative AdS^2_θ and commutative AdS^2 have the same spectrum and thus their c…
The holographic principle, being a generic feature of quantum gravity, should allow for the consideration of dualities other than AdS/CFT. The AdS/BCFT correspondence, in which the dual field theory has local conformal symmetry and is defined on a manifold with boundary, is one such example. Inspired by the quotienting of AdS$_3$ by spacetime isometries in order to construct multiboundary wormholes dual to multipartite CFT$_2$ states, we find that this correspondence can be understood by combining AdS/CFT with some appropriate quotient procedure. Furthermore, in three bulk dimensions, we find …
