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

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

2011-12-21

arxiv.org/abs/1112.5160v1

Physics

High Energy Physics

High Energy Physics - Lattice

7 pages, 5 figures, proceedings of the XXIX International Symposium on Lattice Field Theory - Lattice 2011, July 10-16, 2011,

Scientific paper

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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