The generalized chiral Schwinger model on the two-sphere

Abstract

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.

39 pages, latex, no figures

References in corpus (3)

• Non Perturbative Solutions and Scaling Properties of Vector, Axial--Vector Electrodynamics in $1+1$ Dimensions
• Anomalous dimensions and ghost decoupling in a perturbative approach to the generalized chiral Schwinger model
• Covariant Anomalies and Functional Determinants

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• Topologically Nontrivial Sectors of the Maxwell Field Theory on Algebraic Curves