Breakdown of staggered fermions at nonzero chemical potential

The staggered fermion determinant is complex when the quark chemical potential mu is nonzero. Its fourth root, used in simulations with dynamical fermions, will have phase ambiguities that become acute when Re mu is sufficiently large. We show how to resolve these ambiguities, but our prescription only works very close to the continuum limit. We argue that this regime is far from current capabilities. Other procedures require being even closer to the continuum limit, or fail altogether, because of unphysical discontinuities in the measure. At zero temperature the breakdown is expected when Re mu is greater than approximately half the pion mass. Estimates of the location of the breakdown at nonzero temperature are less certain.Comment: 6 pages RevTeX, 2 figures. Returning to v5 after erroneous replacement. Apologie

Low energy effective action of domain-wall fermion and the Ginsparg-Wilson relation

We derive the effective action of the light fermion field of the domain-wall fermion, which is referred as $q(x)$ by Furman and Shamir. The inverse of the effective Dirac operator turns out to be identical to the inverse of the truncated overlap Dirac operator, except a local contact term which would give the chiral symmetry breaking in the Ginsparg-Wilson relation. This result allows us to relate the light fermion field and the fermion field described by the truncated overlap Dirac operator and to understand the chiral property of the light fermion through the exact chiral symmetry based on the Ginsparg-Wilson relation.Comment: 35 pages, LaTeX2e, references added and updated, minor correction

Reducing Residual-Mass Effects for Domain-Wall Fermions

It has been suggested to project out a number of low-lying eigenvalues of the four-dimensional Wilson--Dirac operator that generates the transfer matrix of domain-wall fermions in order to improve simulations with domain-wall fermions. We investigate how this projection method reduces the residual chiral symmetry-breaking effects for a finite extent of the extra dimension. We use the standard Wilson as well as the renormalization--group--improved gauge action. In both cases we find a substantially reduced residual mass when the projection method is employed. In addition, the large fluctuations in this quantity disappear.Comment: 18 pages, 10 figures, references updated, comments adde

Chiral Fermions on the Lattice through Gauge Fixing -- Perturbation Theory

We study the gauge-fixing approach to the construction of lattice chiral gauge theories in one-loop weak-coupling perturbation theory. We show how infrared properties of the gauge degrees of freedom determine the nature of the continuous phase transition at which we take the continuum limit. The fermion self-energy and the vacuum polarization are calculated, and confirm that, in the abelian case, this approach can be used to put chiral gauge theories on the lattice in four dimensions. We comment on the generalization to the nonabelian case.Comment: 31 pages, 5 figures, two refs. adde