Predicting the Aoki Phase using the Chiral Lagrangian

Abstract

This work is concerned with the phase diagram of Wilson fermions in the mass and coupling constant plane for two-flavor (unquenched) QCD. We show that as the continuum limit is approached, one can study the lattice theory using the continuum chiral Lagrangian, supplemented by additional terms proportional to powers of the lattice spacing. We find two possible phase structures at non-zero lattice spacing: (1) There is an Aoki phase of spontaneously broken flavor and parity, with two massless Goldstone-pions, and a width $\Delta m_0\sim a^3$; (2) There is no spontaneous symmetry breaking, and all three pions have equal mass of order $a$. Present numerical simulations suggest that the former option is realized.

LATTICE98(spectrum), 3 pages, 2 figures, LaTex, uses espcrc2.sty

References in corpus (1)

• Spontaneous Flavor and Parity Breaking with Wilson Fermions

Cited by in corpus (9)

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• Mixing of orthogonal and skew-orthogonal polynomials and its relation to Wilson RMT
• A Possible Aoki Phase for Staggered Fermions
• QCD with two flavors of Wilson fermions: The QCD vacuum, the Aoki vacuum and other vacua
• The Structure of the Aoki Phase at Weak Coupling
• Staggered chiral perturbation theory in the two-flavor case
• 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
• Parity Conservation in Supersymmetric Vector-Like Theories