The ℤ_2 anomaly in some chiral gauge theories

We revisit the simplest Bars-Yankielowicz (BY) model (the psieta model), starting from a model with an additional Dirac pair of fermions in the fundamental representation, together with a complex color-singlet scalar phi coupled to them through a Yukawa interaction. This model possesses a color-flavor-locked 1-form Z(N) symmetry, due to the intersection of the color SU(N) and two nonanomalous U(1) groups. In the bulk, the model reduces to the psi eta model studied earlier when phi acquires a nonzero vacuum expectation value and the extra fermions pair up, get massive and decouple (thus we will call our extended theory as the "X-ray model"), while it provides a regularization of the Z(2) fluxes needed to study the Z(2)anomaly. The anomalies involving the 1-form Z(N) symmetry reduce, for N even, exactly to the mixed Z(2) anomaly found earlier in the psieta model. The present work is a first significant step to clarify the meaning of the mixed Z(2) - [Z(N)^((1)) ]^(2) anomaly found in the psieta and in other BY and Georgi-Glashow type SU(N) models with even N.