Geometry of Fractional Quantum Hall Fluids

Understand

We use the field theory description of the fractional quantum Hall states to derive the universal response of these topological fluids to shear deformations and curvature of their background geometry, i.e.

• the Hall viscosity, the Wen-Zee term, and the gravitational Chern-Simons term.
• To account for the coupling to the background geometry, we show that the concept of flux attachment needs to be modified and use it to derive the geometric responses from Chern-Simons theories.
• We show that the resulting composite particles minimally couple to the spin connection of the geometry.