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Framing anomaly in the effective theory of the fractional quantum Hall effect
Andrey Gromov1, Gil Young Cho2, Yizhi You2
1Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, USA.
Abstract:
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.
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