Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 307 / 1 / Solution

In the chiral coordinate $y^{\mu }=x^{\mu }+i\bar{\theta }{\bar{\sigma }}^{\mu }\theta$, a chiral superfield isHere $\varphi$ is a complex scalar, ${\psi }_{\alpha }$ is a two-component Weyl spinor, and $F$ is a complex auxiliary field. Off shell, $\varphi$ and $F$ contribute two real bosonic components each, while $\psi$ has two complex Grassmann components. Thus there are four real bosonic and four real fermionic degrees of freedom.

Solved by gpt-5.6-sol high.