The AdS2θ/CFT1 Correspondence and Noncommutative Geometry III: Phase Structure of the Noncommutative AdS2θ x S2N
Abstract
The near-horizon noncommutative geometry of black holes, given by AdS2θ x S2N, 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 AdS2θ x S2N 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 AdS2θ x S2N can evaporate only partially to a fuzzy sphere S2N (emergence of time) or to a noncommutative anti-de Sitter spacetime AdS2θ (topology change).