The manifest covariant soliton solutions on noncommutative orbifold $T^{2}/Z_{6}$ and $T^{2}/Z_{3}$

TL;DR

This paper constructs explicit covariant soliton solutions on noncommutative orbifolds $T^2/Z_6$ and $T^2/Z_3$ using elliptic functions, providing a comprehensive framework for such solutions with symmetry properties.

Contribution

It introduces a closed-form construction of covariant projectors on noncommutative orbifolds using elliptic functions, advancing the understanding of soliton solutions in noncommutative field theories.

Findings

Explicit covariant projectors on $T^2/Z_6$ and $T^2/Z_3$ constructed

Projectors possess symmetry and covariant forms under $Z_6$ rotation

Series of covariant soliton solutions presented

Abstract

In this paper, we construct a closed form of projectors on the integral noncommutative orbifold $T^2/Z_6$ in terms of elliptic functions by $GHS$ construction. After that, we give a general solution of projectors on $% T^{2}/Z_{6}$ and $T^{2}/Z_{3}$ with minimal trace and continuous reduced matrix $M(k,q_{0})$.The projectors constructed by us possess symmetry and manifest covariant forms under $Z_{6}$ rotation. Since projectors correspond to the soliton solutions of field theory on the noncommutative orbifold, we thus present a series of corresponding manifest covariant soliton solutions.