THE GENERALIZED CHIRAL SCHWINGER MODEL ON THE 2-SPHERE

A family of theories which interpolate between vector and chiral Schwinger models is studied on the two-sphere S2. The conflict between the loss of gauge invariance and global geometrical properties is solved by introducing a fixed background connection. In this way the generalized Dirac-Weyl operator can be globally defined on S2. The generating functional of the Green functions is obtained by taking carefully into account the contribution of gauge fields with non-trivial topological charge and of the related zero-modes of the Dirac determinant. In the decompactification limit, the Green functions of the flat case are recovered; in particular the fermionic condensate in the vacuum vanishes, at variance with its behaviour in the vector Schwinger model.