Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 306 / 3 / a

A local operator $\mathcal{O}(w,\bar{w})$ is a primary operator of conformal weights $(h,\tilde{h})$ when its operator product expansions with the holomorphic and antiholomorphic stress tensors arewith no more singular poles. Equivalently, under a local conformal transformation it transforms covariantly with holomorphic exponent $h$ and antiholomorphic exponent $\tilde{h}$.