Topological Phases in Neuberger-Dirac operator

Abstract

The response of the Neuberger-Dirac fermion operator $D=\Id + V$ in the topologically nontrivial background gauge field depends on the negative mass parameter $m_0$ in the Wilson-Dirac fermion operator $D_w$ which enters $D$ through the unitary operator $V=D_w(D_w^{†}{D}_w{)}^{-1/2}$. We classify the topological phases of $D$ by comparing its index to the topological charge of the smooth background gauge field. An exact discrete symmetry in the topological phase diagram is proved for any gauge configurations. A formula for the index of D in each topological phase is derived by obtaining the total chiral charge of the zero modes in the exact solution of the free fermion propagator.

27 pages, Latex, 3 figures, appendix A has been revised

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• Numerical study of lattice index theorem usingimproved cooling and overlap fermions
• Perturbation calculation of the axial anomaly of Ginsparg-Wilson fermion
• Quenched chiral logarithms in lattice QCD with exact chiral symmetry
• General bounds on the Wilson-Dirac operator
• Fermion determinant and chiral anomaly on a finite lattice
• Zero-modes of the QED Neuberger Dirac operator