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We consider a $\mathbb{Z}_3$ gauge theory coupled to three degenerate massiveflavors of fermions, which we term "QZD". The spectrum can be computed in $1+1$dimensions using tensor networks. In weak coupling the spectrum is that of theexpected mesons and baryons, although the corrections in weak coupling arenontrivial, analogous to those of non-relativistic QED in 1+1 dimensions. Instrong coupling, besides the usual baryon, the singlet meson is a baryonanti-baryon state. For two special values of the coupling constant, thelightest baryon is degenerate with the lightest octet meson, and the lightestsinglet meson, respectively.

Mass gaps of a $\mathbb{Z}_3$ gauge theory with three fermion flavors in 1 + 1 dimensions