Symmetry and Symmetry Restoration of Lattice Chiral Fermion in the Overlap Formalism

Three aspects of symmetry structure of lattice chiral fermion in the overlap formalism are discussed. By the weak coupling expansion of the overlap Dirac operator, the axial anomaly associated to the chiral transformation proposed by Lüscher is evaluated and is shown to have the correct form of the topological charge density for perturbative backgrounds. Next we discuss the exponential suppression of the self-energy correction of the lightest 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.