CHIRAL SYMMETRY AND OPERATOR MIXING IN LATTICE SU(N) THIRRING MODEL WITH SHIFT SYMMETRY

Abstract

We formulate lattice SU (N) Thirring model in which two Wilson fermions describe the respective left- and right-handed components of the Dirac fermion in the continuum model. Only chirally projected half components of the Wilson fermions have four-fermion interaction. As to their non-interacting components, there exist shift symmetries discussed by Golterman and Petcher. Axial U (1) Ward-Takahashi identity is examined by weak coupling expansion. It is shown in all orders of the weak coupling expansion that the chiral limit is achieved by simply setting fermion bare mass equal to zero, and that a lattice operator has no mixing due to the Wilson masses with the operators of wrong chiral representation and of lower dimensionality.