The AdS^2_{\theta}/CFT_1 Correspondence and Noncommutative Geometry III: Phase Structure of the Noncommutative AdS^2_{\theta} x S^2_N

TL;DR

This paper explores the phase transitions and topology changes in the noncommutative geometry of black hole horizons modeled by AdS^2_{ heta} x S^2_N, revealing emergent geometries and evaporation processes.

Contribution

It presents a detailed analysis of the phase structure and topology change transitions in the noncommutative AdS^2_{ heta} x S^2_N geometry within Yang-Mills matrix models.

Findings

Identification of a phase transition between geometric and matrix phases.

Evidence for topology change involving space and time directions.

Partial evaporation of the noncommutative horizon to fuzzy spheres or AdS spacetimes.

Abstract

The near-horizon noncommutative geometry of black holes, given by AdS^2_{\theta} x S^2_N, 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 AdS^2_{\theta} x S^2_N 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 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 anti-de Sitter spacetime AdS^2_{\theta} (topology change).