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Abstract: In this paper we link the physics of topological nonlinear {\sigma} modelswith that of Chern-Simons insulators. We show that corresponding to every2n-dimensional Chern-Simons insulator there is a n-1-dimensional topologicalnonlinear {\sigma} model with the Wess-Zumino-Witten term. Breaking internalsymmetry in these nonlinear {\sigma} models leads to nonlinear {\sigma} modelswith the {\theta} term. This is analogous to the dimension reduction leadingfrom 2n-dimensional Chern-Simons insulators to 2n-1 and 2n-2-dimensionaltopological insulators protected by discrete symmetries. The correspondencedescribed in this paper allows one to derive the topological term in a theoryinvolving fermions and order parameters we shall referred to them as-fermion-{\sigma} models- when the conventional gradient-expansion methodfails. We also discuss the quantum number of solitons in topological nonlinear{\sigma} model and the electromagnetic action of the 2n-1-dimensionaltopological insulators. Throughout the paper we use a simple model toillustrate how things work.



Author: Hong Yao, Dung-Hai Lee

Source: https://arxiv.org/







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