I'm trying to understand David Tong's http://www.damtp.cam.ac.uk/user/tong/gaugetheory.html, specifically the discussion around page 92 where he's arguing that a different symmetry group may the group of QCD, namely G′=SU(N)/ZN instead of G=SU(N).
I understand that having G′ as a group leads to a different quantization of the θ term, but I want to know if this is really the crucial aspect? Namely, how does the cyclic group ZN act on the fundamental fields (quarks, gluons)? Can anybody show this invariance to me at the level of the Lagrangian? I'm a bit confused so even the most pedestrian computation would help :)