The AdS^2_{\theta}/CFT_1 Correspondence and Noncommutative Geometry II: Noncommutative Quantum Black Holes

TL;DR

This paper constructs a noncommutative AdS^2_{ heta} black hole model within a matrix framework, revealing a phase diagram with gravitational, geometric, and Yang-Mills phases, and explores phase transitions including Hawking radiation.

Contribution

It introduces a novel noncommutative AdS^2_{ heta} black hole model and analyzes its phase structure using a Yang-Mills matrix model with two Myers terms, highlighting phase transitions.

Findings

Identification of three distinct phases in the matrix model.

Description of Hawking process as a phase transition.

Construction of a noncommutative sigma model for phase transitions.

Abstract

In this article we present the construction of noncommutative AdS^2_{\theta} 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_{\theta} 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_{\theta} black hole), 2) A geometric phase (AdS^2_{\theta} 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 non-linear sigma model describing the transition of the dilaton field between the gravitational and geometrical phases is also constructed.