Optimal Lattice Domain-Wall Fermions

Abstract

I show that the conventional formulations of lattice domain-wall fermion with any finite N s (in the fifth dimension) do not preserve the chiral symmetry optimally and propose a new action which preserves the chiral symmetry optimally for any finite N s .

Möbius Fermions

“…The optimal choice for the approximation to the sign function are the Zolotarev coefficients [8]. In other words, of all possible choices for the coefficients, Zolotarev will achieve the smallest residual mass.…”

“…This work led to two concrete realizations of lattice fermions with chiral symmetry. The domain wall fermions [5,6,7,8] and the overlap fermions [9,10,11,12,13].…”

Light quark masses, chiral condensate and quark-gluon condensate in quenched lattice QCD With exact chiral symmetry

“…However, it has been shown [5] that the conventional DWF with any finite N s does not preserve the chiral symmetry optimally for any gauge background.…”

“…Exact chiral symmetry on the lattice was pioneered by Kaplan [1] with his proposal of domain-wall fermions (DWF) on the 5-dimensional lattice, in which the fifth dimension (internal flavor space) is discretized with N s sites (flavors) and lattice spacing a 5 . Although the initial motivation was to provide a nonperturbative formulation of chiral gauge theories, the idea turns out to be natural and well-defined for vector-like gauge theories (e.g.…”

“…has proposed a new DWF action [5,6] such that the quark propagator preserves the chiral symmetry optimally for any N s and background gauge field. Further, its effective 4D lattice Dirac operator (with any N s and m q ) for internal fermion loops is exponentially-local for sufficiently smooth gauge backgrounds [7].…”