Framing anomaly in the effective theory of the fractional quantum Hall effect

We consider the geometric part of the effective action for the fractional quantum Hall effect (FQHE). It is shown that accounting for the framing anomaly of the quantum Chern-Simons theory is essential to obtain the correct gravitational linear response functions. In the lowest order in gradients, t...

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Bibliographic Details
Published in:Physical review letters 2015-01, Vol.114 (1), p.016805-016805, Article 016805
Main Authors: Gromov, Andrey, Cho, Gil Young, You, Yizhi, Abanov, Alexander G, Fradkin, Eduardo
Format: Article
Language:English
Subjects:
Accounting
Anomalies
Framing
Gravitation
Gravitation theory
Quantum Hall effect
Response functions
Viscosity
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Summary:We consider the geometric part of the effective action for the fractional quantum Hall effect (FQHE). It is shown that accounting for the framing anomaly of the quantum Chern-Simons theory is essential to obtain the correct gravitational linear response functions. In the lowest order in gradients, the linear response generating functional includes Chern-Simons, Wen-Zee, and gravitational Chern-Simons terms. The latter term has a contribution from the framing anomaly which fixes the value of thermal Hall conductivity and contributes to the Hall viscosity of the FQH states on a sphere. We also discuss the effects of the framing anomaly on linear responses for non-Abelian FQH states.
ISSN:0031-9007
1079-7114
DOI:10.1103/physrevlett.114.016805