A primary operator of <conformal weight> $(h,\widetilde h)$ transforms under $z\mapsto w(z)$ as
$$
\widetilde{\mathcal O}(w,\bar w)
=\left(\frac{dw}{dz}\right)^{-h}
\left(\frac{d\bar w}{d\bar z}\right)^{-\widetilde h}
\mathcal O(z,\bar z).
$$
The derivative $\partial X$ is a primary of weight $(1,0)$, and $\bar\partial X$ is a primary of weight $(0,1)$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 306 / 2 / c / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-306/2/c/solution