Abstract
We focus on the four-dimensional central-branch Wilson fermion, which makes good use of six species at the central branch of the Wilson Dirac spectrum and possesses the extra $U(1)_{\overline V}$ symmetry. With introducing new insights we discuss the prohibition of additive mass renormalization for all the six species, SSB of $U(1)_{\overline V}$ in strong-coupling QCD, the absence of the sign problem, and the usefulness for many-flavor QCD simulation. We then construct several varieties of the central-branch fermions and study their properties. In particular, we investigate the two-flavor version, where the Dirac spectrum has seven branches and two species live at the central branch. Although the hypercubic symmetry is broken, the other symmetries are the same as those of the original one. We study this setup in terms of lattice perturbation theory, strong-coupling QCD, the absence of sign problem, and the parameter tuning for Lorentz symmetry restoration. By comparing the properties of the original and two-flavor version, we find that the existence of hypercubic symmetry as well as $U(1)_{\overline V}$ is essential for the absence of additive mass renormalization of all the central-branch species. As the other two-flavor version, we investigate the central-branch staggered-Wilson fermion, which is obtained from the eight-flavor central-branch Wilson fermion via spin diagonalization. We argue that it is free from any additive mass renormalization and is regarded as a minimally doubled fermion with less symmetry breaking.
Highlights
In the last four decades theoretical physicists have successfully been studying nonperturbative aspects of quantum field theories including Yang-Mills theory and quantum chromodynamics (QCD) by use of lattice gauge theory [1,2]
The hypercubic symmetry is broken, the other symmetries are the same as those of the original one. We study this setup in terms of lattice perturbation theory, strong-coupling QCD, the absence of sign problem, and the parameter tuning for Lorentz symmetry restoration
We study the properties of the two-flavor version, including the additive mass renormalization, spontaneous symmetry breaking (SSB) of parity and Uð1ÞVsymmetry in the strong-coupling lattice QCD, the absence of the sign problem and the parameter tuning procedure for Lorentz symmetry restoration
Summary
In the last four decades theoretical physicists have successfully been studying nonperturbative aspects of quantum field theories including Yang-Mills theory and quantum chromodynamics (QCD) by use of lattice gauge theory [1,2]. Staggered fermion keeps a Uð1Þ subgroup of chiral symmetry and eliminate OðaÞ errors, where the degeneracy of four flavors requires the rooting trick for realistic (2 þ 1)-flavor QCD [13,14,15,16,17,18,19] In these years, several new approaches to lattice fermion formulations have been investigated: The Wilson term in Wilson fermion can be generalized to “flavored-mass terms.”. We first perform comprehensive study on the formulation with introducing several new insights, where we discuss its construction, the prohibition of additive mass renormalization and its interpretation in terms of ’t Hooft anomaly, spontaneous symmetry breaking in the strong-coupling QCD, the absence or the solution of the sign problem for quark determinant, and the possibility of its practical use.
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