The generalized chiral Schwinger model on the two-sphere

Details The generalized chiral Schwinger model on the two-sphere The generalized chiral Schwinger model on the two-sphere

1994-11-30

arxiv.org/abs/hep-th/9411229v1

Nucl.Phys. B439 (1995) 327-366

Physics

High Energy Physics

High Energy Physics - Theory

39 pages, latex, no figures

Scientific paper

10.1016/0550-3213(95)00044-S

A family of theories which interpolate between vector and chiral Schwinger models is studied on the two--sphere $S^{2}$. 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 $S^{2}$. 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.

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