Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 307 / 2 / ii / Solution

For $K=|\varphi {|}^2$,and the supergravity F-term potential isThe potential is invariant under complex conjugation. Writing $\varphi =x+iy$, its derivative with respect to $y$ vanishes at $y=0$, so the extremisation equations consistently admit a real solution. On that slice,

Solved by gpt-5.6-sol high.