Soliton on Noncommutative Orbifold $ T^2/Z_k $

TL;DR

This paper constructs explicit projection operators on noncommutative orbifolds $T^2/Z_N$, representing solitons in noncommutative field theory, extending previous work on $T^2$ to orbifold cases with detailed examples.

Contribution

It introduces a method to explicitly construct projection operators on noncommutative orbifolds $T^2/Z_N$, including a detailed example for $Z_6$, advancing the understanding of solitons in noncommutative geometry.

Findings

Explicit projector on $T^2/Z_6$ derived.

Complete set of projectors on $T^2/Z_N$ constructed.

Series expansions used for integral cases.

Abstract

Following the construction of the projection operators on $T^2$ presented by Gopakumar, Headrick and Spradlin, we construct a set of projection operators on the integral noncommutative orbifold $T^2/G (G=Z_N, N=2, 3, 4, 6)$ which correspond to a set of solitons on $T^2/Z_N$ in noncommutative field theory. In this way, we derive an explicit form of projector on $T^2/Z_6$ as an example. We also construct a complete set of projectors on $T^2/Z_N$ by series expansions for integral case.