The restoration of gauge symmetry in the overlap formalism

The overlap formalism is one of the most promising approaches to the lattic e chiral gauge theory. The gauge symmetry violation on the lattice resides minimally in the phase of the fermion determinant. The crucial issue is whe ther the gauge symmetry is restored in the continuum limit for the anomaly- free fermion content. We propose some specific criteria for the gauge symme try restoration and investigate them numerically for the 2D chiral U(1) gau ge theory.