Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect

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.

5 pages, v3 contains the Erratum on the value of the orbital spin variance

References in corpus (5)

• Thermal Hall Effect and Geometry with Torsion
• Low-energy effective theory in the bulk for transport in a topological phase
• Density-curvature response and gravitational anomaly
• Topological central charge from Berry curvature: gravitational anomalies in trial wavefunctions for topological phases
• Geometry of Fractional Quantum Hall Fluids

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