出版社：SISSA, Scuola Internazionale Superiore di Studi Avanzati
摘要：The QCD partition function for the Wilson Dirac operator, DW, at nonzero lattice spacing a can be expressed in terms of a chiral Lagrangian as a systematic expansion in the quark mass, the momentum and a2. Starting from this chiral Lagrangian we obtain an analytical expression for the spectral density of γ5(DW +m) in the microscopic domain. It is shown that the γ5-Hermiticity of the Dirac operator necessarily leads to a coefficient of the a2 term that is consistent with the existence of an Aoki phase. The transition to the Aoki phase is explained, and the interplay of the index of DW and nonzero a is discussed. We formulate a random matrix theory for the Wilson Dirac operator with index ν (which, in the continuum limit, becomes equal to the topological charge of gauge field configurations). It is shown by an explicit calculation that this random matrix theory reproduces the a2-dependence of the chiral Lagrangian in the microscopic domain, and that the sign of the a2-term is directly related to the γ5-Hermiticity of DW.
