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Soliton Solutions on Noncommutative Orbifold $T^{2N}/G$

Hui Deng·Bo-Yu Hou·Guo-Fang Shi·Kang-Jie Shi·Rui-Hong Yue·Hua-Hui Xiong
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Abstract

In this paper, we construct the common eigenstates of "translation" operators $\{U_{s}\}$ and establish the generalized $Kq$ representation on integral noncommutative torus $T^{2N}$. We then study the finite rotation group $G$ in noncommutative space as a mapping in the $Kq$ representation and prove a Blocking Theorem. We finally obtain the complete set of projection operators on the integral noncommutative orbifold $T^{2N}/G$ in terms of the generalized $Kq$ representation. Since projectors are soliton solutions on noncommutative space in the limit $α^{\prime}B_{ij}\to \infty (Θ_{ij}/α^{\prime}\to 0)$, we thus obtain all soliton solutions on that orbifold $T^{2N}/G$.

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Hui Deng, Bo-Yu Hou, Guo-Fang Shi, Kang-Jie Shi, Rui-Hong Yue, Hua-Hui Xiong. 2004-05-14. Soliton Solutions on Noncommutative Orbifold $T^{2N}/G$. https://arxiv.org/abs/hep-th/0405130

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