Translation and rotation invariance make the two-point function depend only on $|x_{12}|$. Scale covariance then fixes its power, and inversion or special-conformal invariance requires equal dimensions for a nonzero scalar two-point function. For identical <primary operator>[scalar primary operators],
$$
\boxed{\langle O(x_1)O(x_2)\rangle
=\frac{C_2}{|x_{12}|^{2\Delta}}}.
$$
Only the normalization $C_2$ depends on the operator convention.

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 / i / Solution

 Solution

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