The AdS𝜃2/CFT1 correspondence and noncommutative geometry III: Phase structure of the noncommutative AdS𝜃2 × 𝕊N2

Abstract

The near-horizon noncommutative geometry of black holes, given by [Formula: see text], 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 [Formula: see text] 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 [Formula: see text] can evaporate only partially to a fuzzy sphere [Formula: see text] (emergence of time) or to a noncommutative anti-de Sitter space–time [Formula: see text] (topology change).