Instantons in (1 + 1) -dimensional Abelian gauge theories

We study the Abelian Higgs model in 1 + 1 dimensions with the addition of a fermion of arbitrary charge g to understand the effect of instantons on the gauge and chiral structure of the model. Semiclassical approximations are used assuming a small instanton density. Without fermions, the global gauge symmetry is found to be restored, resulting in a linearly rising potential between static charges ( +- Q) and a complete screening of integral charges (Q/e = integer with e the scalar charge). This gauge structure persists with the addition of a massive fermion. The spectrum of fermion bound states and the stability of the theta vacuums are discussed. For a massless fermion, the gauge symmetry is spontaneously broken. We explicitly show that the chiral symmetry is also spontaneously broken, but that the Nambu-Goldstone pole decouples from the gauge-invariant sector of the theory