On the connection between the principal chiral model and the multiflavour chiral Gross-Neveu model

The infinite flavour limit of the multiflavour chiral Cross-Neveu (MCGN) partition function is shown to be equal to the principal chiral σ-model (PCM) partition function where in addition one integrates over twisted boundary conditions. This last interpretation restricts the space of states to the left (or right) singlet sector. In the course of this derivation, a rigorous paramagnetic inequality for the Dirac determinant is proved. The critical (conformal invariant) points of the MCGN are investigated in connection with critical WZW σ-models. (orig.)