Quantum Hall Effect, Bosonization and Chiral Actions in Higher Dimensions

6th International Symposium on Quantum Theory and Symmetries

Karabali, Dimitra^1

Department of Physics and Astronomy, Lehman College, CUNY, Bronx, NY 10468, United States^1

关键词: Higher dimensions;    Higher-dimensional;    Landau levels;    Non-Abelian gauge;    Non-commutative;    Nonrelativistic;    Quantum Hall systems;    Semiclassical limit;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/462/1/012023/pdf
DOI  :  10.1088/1742-6596/462/1/012023

来源: IOP

【 摘 要 】

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. This can be used to write down a bosonized noncommutative field theory describing the interactions of higher dimensional nonrelativistic fermions with abelian or nonabelian gauge fields in the lowest Landau level. This general approach is applied explicitly to the case of QHE on CPk. It is shown that in the semiclassical limit the effective action contains a bulk Chern-Simons type term whose anomaly is exactly canceled by a boundary term given in terms of a chiral, gauged Wess-Zumino-Witten action suitably generalized to higher dimensions.