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We study the low-lying eigenmodes of the lattice overlap Dirac operator for SV(Nc) gauge theories with Nc=2, 3, 4 and 5 colors. We define a fermionic topological charge from the zero modes of this operator and show that, as Nc grows, any disagreement with the topological charge obtained by cooling the fields becomes rapidly less likely. By examining the fields where there is a disagreement, we are able to show that the Dirac operator does not resolve instantons below a critical size of about ρ≃2.5a, but resolves the larger, more physical instantons. We investigate the local chirality of the near-zero modes and how it changes as we go to larger Nc. We observe that the local chirality of these modes, which is prominent for SU(2) and SU(3), becomes rapidly weaker for larger N c and is consistent with disappearing entirely in the limit of N c = ∞. We find that this is not simply due to the observed disappearance of small instantons at larger Nc. © 2002 The American Physical Society

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Topology and chiral symmetry breaking in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">SU</mml:mi><mml:mrow><mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:math>gauge theories

Topology and chiral symmetry breaking inSU(Nc)gauge theories