The AdS^2_{\theta}/CFT_1 Correspondence and Noncommutative Geometry III: Phase Structure of the Noncommutative AdS^2_{\theta} x S^2_N
Abstract
The nearhorizon noncommutative geometry of black holes, given by AdS^2_{\theta} x S^2_N, is discussed and the phase structure of the corresponding YangMills 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_{\theta} x S^2_N phase (discrete spectrum) and a YangMills 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 nearhorizon geometry AdS^2_{\theta} x S^2_N can evaporate only partially to a fuzzy sphere S^2_N (emergence of time) or to a noncommutative antide Sitter spacetime AdS^2_{\theta} (topology change).
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.01010
 Bibcode:
 2021arXiv210901010Y
 Keywords:

 High Energy Physics  Theory
 EPrint:
 This is the third part of a threeparts 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 [hepth]. Part II:arXiv:2109.00380 [hepth]