Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 305 / 2 / vi / Solution

Since ${\partial }_{\mu }{K}^{\mu }=\mathrm{Tr}(F_{\mu \nu }{}^{\star }{F}^{\mu \nu })$, defineThe anomaly equation gives ${\partial }_{\mu }{\tilde{J}}_A^{\mu }=0$. The price is that the Chern-Simons current $K^{\mu }$ is not gauge invariant, so neither is ${\tilde{J}}_A^{\mu }$.

Solved by gpt-5.6-sol high.