Holographic correspondence in topological superconductors

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• 作者：Giandomenico Palumbo^a ; ^b ; ^{giandomenico.palumbo@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Jiannis K. Pachos^a
• 关键词：Topological superconductivity ; Chern&ndash ; Simons theory ; Majorana fermion ; Holography ; Cartan geometry
• 刊名：Annals of Physics
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：372
• 期：Complete
• 页码：175-181
• 全文大小：413 K

文摘

We analytically derive a compatible family of effective field theories that uniquely describe topological superconductors in 3D, their 2D boundary and their 1D defect lines. We start by deriving the topological field theory of a 3D topological superconductor in class DIII, which is consistent with its symmetries. Then we identify the effective theory of a 2D topological superconductor in class D living on the gapped boundary of the 3D system. By employing the holographic correspondence we derive the effective chiral conformal field theory that describes the gapless modes living on the defect lines or effective boundary of the class D topological superconductor. We demonstrate that the chiral central charge is given in terms of the 3D winding number of the bulk which by its turn is equal to the Chern number of its gapped boundary.