The AdS𝜃2/CFT1 correspondence and noncommutative geometry II: Noncommutative quantum black holes

Abstract

In this paper, we present the construction of noncommutative [Formula: see text] 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 [Formula: see text] 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 ([Formula: see text] black hole), (2) a geometric phase ([Formula: see text] background) and (3) a Yang–Mills phase. The Hawking process is therefore seen as an exotic line of discontinuous transitions between the gravitational and geometrical phases. Alternatively, a noncommutative nonlinear sigma model describing the transition of the dilaton field between the gravitational and geometrical phases is also constructed.