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arXiv · 1410.6812

Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect

Andrey Gromov·Gil Young Cho·Yizhi You·Alexander G. Abanov·Eduardo Fradkin
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Abstract

We consider the geometric part of the effective action for Fractional Quantum Hall Effect (FQHE). It is shown that accounting for the framing anomaly of the quantum Chern-Simons theory is essential to the obtain 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.

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Andrey Gromov, Gil Young Cho, Yizhi You, Alexander G. Abanov, Eduardo Fradkin. 2015-03-25. Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect. https://doi.org/10.1103/physrevlett.114.016805

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