Journal
PHYSICAL REVIEW LETTERS
Volume 114, Issue 1, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.114.016805
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Funding
- Kavli Institute for Theoretical Physics (KITP)
- Simons Foundation
- IRONIC14 program
- National Science Foundation (NSF) at Stony Brook University [DMR-1206790, DMR-1064319, DMR 1408713]
- KITP [PHY11-25915]
- University of Illinois
- Direct For Mathematical & Physical Scien
- Division Of Materials Research [1206790, 1064319, 1408713] Funding Source: National Science Foundation
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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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