Topology, Random Matrix Theory and the spectrum of the Wilson Dirac operator

Source: arXiv

ABSTRACT We study the spectrum of the hermitian Wilson Dirac operator in the
epsilon-regime of QCD in the quenched approximation and compare it to
predictions from Wilson Random Matrix Theory. Using the distributions of single
eigenvalues in the microscopic limit and for specific topological charge
sectors, we examine the possibility of extracting estimates of the low energy
constants which parametrise the lattice artefacts in Wilson chiral perturbation
theory. The topological charge of the field configurations is obtained from a
field theoretical definition as well as from the flow of eigenvalues of the
hermitian Wilson Dirac operator, and we determine the extent to which the two
are correlated.

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