Angles in Fuzzy Disc and Angular Noncommutative Solitons

TL;DR

This paper introduces a novel way to define angles on fuzzy discs using phase operators, constructs angular solitons, and explores applications in noncommutative gravity, black hole microstates, and experimental physics.

Contribution

It presents a new angular framework for fuzzy discs using phase operators and constructs fan-shaped solitons, extending noncommutative geometry applications.

Findings

Defined angles on fuzzy discs via phase operators.

Constructed fan-shaped soliton solutions on fuzzy discs.

Suggested links to black hole microstates and experimental tests.

Abstract

The fuzzy disc, introduced by the authors of Ref.[1], is a disc-shaped region in a noncommutative plane, and is a fuzzy approximation of a commutative disc. In this paper we show that one can introduce a concept of angles to the fuzzy disc, by using the phase operator and phase states known in quantum optics. We gave a description of a fuzzy disc in terms of operators and their commutation relations, and studied properties of angular projection operators. A similar construction for a fuzzy annulus is also given. As an application, we constructed fan-shaped soliton solutions of a scalar field theory on a fuzzy disc, which corresponds to a fan-shaped D-brane. We also applied this concept to the theory of noncommutative gravity that we proposed in Ref.[2]. In addition, possible connections to black hole microstates, holography and an experimental test of noncommutativity by laser physics are suggested.