Quantum Hall effect in higher dimensions, matrix models and fuzzy geometry
Quantum Hall effect in higher dimensions, matrix models and fuzzy geometry
复制标题
高维量子霍尔效应、矩阵模型和模糊几何
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
V. Nair
中科院分区：
文献类型：
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作者：
D. Karabali;V. Nair
我们简要回顾了高维量子霍尔效应及其与模糊空间的关系。对于量子霍尔系统，最低朗道能级动力学由一维矩阵作用给出，其大的N极限产生描述高维量子霍尔液滴规范相互作用的有效作用。体作用量是一种Chern-Simons类型的项，它的反常被用手征、规范的Wess-Zumino-Witten理论给出的边界作用量精确地抵消，该理论适合推广到更高的维度。我们认为，Chern-Simons作用量中的规范场可以理解为对矩阵理论的大N极限的不同取值方式的参数化。解释了这些想法与模糊重力的可能相关性。文中还简要讨论了它的其他应用。
We give a brief review of the quantum Hall effect in higher dimensions and its relation to fuzzy spaces. For a quantum Hall system, the lowest Landau level dynamics is given by a one-dimensional matrix action whose large N limit produces an effective action describing the gauge interactions of a higher dimensional quantum Hall droplet. The bulk action is a Chern–Simons type term whose anomaly is exactly cancelled by the boundary action given in terms of a chiral, gauged Wess–Zumino–Witten theory suitably generalized to higher dimensions. We argue that the gauge fields in the Chern–Simons action can be understood as parametrizing the different ways in which the large N limit of the matrix theory is taken. The possible relevance of these ideas to fuzzy gravity is explained. Other applications are also briefly discussed.