Symmetry and symmetry restoration of lattice chiral fermions in the overlap formalism

Three aspects of the symmetry structure of lattice chiral fermions in the o verlap formalism are discussed. By the weak coupling expansion of the overl ap Dirac operator, the axial anomaly associated to the chiral transformatio n proposed by Luscher is evaluated and is shown to have the correct form of the topological charge density for perturbative backgrounds. Next we discu ss the exponential suppression of the self-energy correction of the lightes t mode in the domain-wall fermion/truncated overlap. Finally, we consider a supersymmetric extension of the overlap formula in the case of the chiral multiplet and examine the symmetry structure of the action.