Central charge from adiabatic transport of cusp singularities in the quantum Hall effect

Understand

We study quantum Hall (QH) states on a punctured Riemann sphere.

• We compute the Berry curvature under adiabatic motion in the moduli space in the large N limit.
• The Berry curvature is shown to be finite in the large N limit and controlled by the conformal dimension of the cusp singularity, a local property of the mean density.
• Utilizing exact sum rules obtained from a Ward identity, we show that for the Laughlin wave function, the dimension of a cusp singularity is given by the central charge, a robust geometric response coefficient in the QHE.