Domain-Wall Fermion with $R_5$ Symmetry

Abstract

We present the domain-wall fermion operator which is reflection symmetric in the fifth dimension, with the approximate sign function $S(H)$ of the effective 4-dimensional Dirac operator satisfying the bound $|1-S(\lambda )|\le 2d_Z$ for ${\lambda }^2\in [{\lambda }_{min}^2,{\lambda }_{max}^2]$, where $d_Z$ is the maximum deviation $|1-\sqrt{x}{R}_Z(x){|}_{\max }$ of the Zolotarev optimal rational polynomial $R_Z(x)$ of $1/\sqrt{x}$ for $x\in [1,{\lambda }_{max}^2/{\lambda }_{min}^2]$, with degrees $(n-1,n)$ for $N_s=2n$, and $(n,n)$ for $N_s=2n+1$.

Comments: This work is dedicated to late Professor James S. Ball