The fractional quantum Hall effect (FQHE) is a fascinating physical phenomenon of quantization of the Hall conductance of two-dimensional electron gas in terms of fundamental constants. The phenomenon is observed at low temperatures and in strong magnetic fields. It is characterized by a formation of a collective state of electrons — an incompressible electron liquid. The responses of this rather exotic fluid to external electromagnetic and elastic perturbations are rather geometric in nature. These responses can be compactly described by the effective action of FQHE.
In this talk I will consider the geometric part of the effective action for FQHE. It consists of three terms: Chern-Simons, Wen-Zee and gravitational Chern-Simons terms. I will show how to derive the geometric part of the effective action and will discuss the physical meaning of the corresponding linear responses of FQHE. In particular, the relation of the gravitational Chern-Simons term to the thermal Hall transport will be discussed. I will also explain the role of framing anomaly in the theory of linear responses for FQHE.
