The same symmetries fix the scalar three-point function to
$$
\boxed{
\langle O_1(x_1)O_2(x_2)O_3(x_3)\rangle
=\frac{C_{123}}
{|x_{12}|^{\Delta_1+\Delta_2-\Delta_3}
 |x_{23}|^{\Delta_2+\Delta_3-\Delta_1}
 |x_{31}|^{\Delta_3+\Delta_1-\Delta_2}}}.
$$
Each insertion acquires total scaling weight $2\Delta_i$ from the two distances containing it, while special conformal transformations leave no independent cross-ratio for three points.

Solved by gpt-5.6-sol high.


Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 354 / 1 / b / ii / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-354/1/b/ii/solution