Understanding the Aoki phase
V. Azcoiti, G. Di Carlo, E. Follana, A. Vaquero
TL;DR
This paper investigates the vacuum structure of QCD with Wilson fermions, exploring the conditions for the Aoki phase and analyzing the implications of different regularizations, including Ginsparg-Wilson.
Contribution
It provides a detailed analysis of the Aoki phase using the p.d.f. formalism and compares Wilson and Ginsparg-Wilson regularizations, revealing conditions for phase emergence or absence.
Findings
Aoki phases can emerge under certain assumptions with Wilson fermions.
Eigenvalues of the Dirac-Wilson operator satisfy specific sum rules.
Ginsparg-Wilson regularization shows no parity or flavor breaking phases at non-zero mass.
Abstract
The vacuum structure of QCD with two degenerated flavours of Wilson fermions is discussed by means of the p.d.f. (probability distribution function) formalism. Under certain assumptions, either new phases related to Aoki's appear, characterized by a non-vanishing expectation value of the condensate , enriching the standard picture of the QCD vacuum structure with Wilson fermions; or the eigenvalues of the Dirac-Wilson operator must comply with a non-trivial, infinite set of sum rules, enforcing the currently accepted structure of the Aoki vacuum. The same scenario is analyzed using the Ginsparg-Wilson regularization. In this case, the absence of any parity and/or flavour breaking phase is proved for a non-zero value of the fermion mass.
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Taxonomy
TopicsStatistical Mechanics and Entropy · High-Energy Particle Collisions Research · Complex Systems and Time Series Analysis