QCD with two flavors of Wilson fermions: The QCD vacuum, the Aoki vacuum and other vacua

Abstract

We discuss the vacuum structure of QCD with two flavors of Wilson fermions. We derive two possible scenarios: (i) If the spectral density ${\rho }_U(\lambda ,\kappa )$ of the overlap hamiltonian in a fixed background gauge field is not symmetric in $\lambda$, Hermiticity is violated and Hermiticity violation effects could influence numerical determinations of the $\eta$ meson mass if we are not near enough to the continuum limit, where Hermiticity should be recovered; (ii) otherwise we argue that, under certain assumptions, new phases appear beside the Aoki phase, which can be characterized by a nonvanishing vacuum expectation value of $i{\bar{\psi }}_u{\gamma }_5{\psi }_u+i{\bar{\psi }}_d{\gamma }_5{\psi }_d$, and with vacuum states that cannot be connected with the Aoki vacua by parity-flavor symmetry transformations. Quenched numerical simulations suggest that the second scenario is more likely realized.

arXiv comment9 pages, 6 figures, to be published in Physical Review D1

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Cited by in corpus (14)

• Spectrum of the Wilson Dirac Operator at Finite Lattice Spacings
• On the consistency of the Aoki-phase
• Exploration of SU(N_c) gauge theory with many Wilson fermions at strong coupling
• Phase structure for lattice fermions with flavored chemical potential terms
• QCD phase diagram with 2-flavor lattice fermion formulations
• Strong-coupling Analysis of Parity Phase Structure in Staggered-Wilson Fermions
• Kondo effect with Wilson fermions
• Chiral Dynamics With Wilson Fermions
• Elucidating the Vacuum Structure of the Aoki Phase
• Phase structure of a generalized Nambu Jona-Lasinio model with Wilson fermions in the mean field or large $N$-expansion
• Impossibility of spontaneous vector flavor symmetry breaking on the lattice
• Non-${\gamma }_5$hermiticity fermions in two dimensions
• Understanding the Aoki phase
• The Aoki phase revisited