Speaker
Jacobus Verbaarschot
(Stony Brook University)
Description
The QCD partition function for the Wilson Dirac operator, $D_W$, at finite lattice spacing $a$ can be expressed
in terms of a chiral Lagrangian as a systematic expansion in the mass, the momentum and $a^2$. Starting
from this chiral Lagrangian we obtain an analytical expression for the spectral density of $\gamma_5 D_W$ in the microscopic domain (also known as the $]epsilon$-domain). It is shown that the $\gamma_5$-Hermiticity of the Dirac operator necessarily leads to the sign of the coefficient of the $a^2$ term that allows an Aoki phase. The transition to the Aoki phase is explained in detail, and the interplay of topological charge and finite $a$ is discussed. Finally, we formulate a random matrix theory for the Wilson Dirac operator in the sector of topological charge $\nu$. It is shown by an explicit calculation that this random matrix theory reproduces the $a^2$-dependence of the chiral Lagrangian in the microscopic domain and that the sign the $a^2$-term is directly related to the
$\gamma_5$-hermiticity of $D_W$.
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Primary authors
Jacobus Verbaarschot
(Stony Brook University)
Prof.
Kim Splittorff
(Niels Bohr Institute)
Prof.
Poul Henrik Damgaard
(Niels Bohr International Academy and Neils Bohr Institute)
