Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 303 / 2 / e / ii

No. With only ${\lambda }_0{\varphi }^6$, the free energy has an exact Z2 symmetry $\varphi \mapsto -\varphi$. Integrating out fast modes and rescaling preserve that symmetry, whereas ${\varphi }^5$ is odd. Therefore no five-point vertex and no correction to $\gamma (\zeta )$ can be generated at any order in ${\lambda }_0$.