Central Charge from Adiabatic Transport of Cusp Singularities in the Quantum Hall Effect

We identify the central charge of fractional quantum Hall (FQH) states by studying adiabatic evolution in the parameter space of singular surfaces. In particular, we study FQH states on a punctured sphere and compute the Berry curvature under adiabatic motion of cusp singularities at the punctures. The Berry curvature is finite in the large N limit and completely controlled by the central charge, a robust geometric response coefficient.