A. Zee, Quantum Field Theory in a Nutshell · Problem VIII.3.1

Field Theory Redux

Physics — QFT

Problem

Consider

\mathcal{L} = \frac{1}{2}\left[(\partial \phi_1)^2 + (\partial \phi_2)^2\right] - \lambda(\phi_1^4 + \phi_2^4) - g\phi_1^2\phi_2^2

We have taken the

O(2)

theory from chapter I.10 and broken the symmetry explicitly. Work out the renormalization group flow in the

(\lambda - g)

plane and draw your own conclusions.