Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
1998-01-19
Phys.Lett. B427 (1998) 125-131
Physics
High Energy Physics
High Energy Physics - Lattice
9 pages, 1 figure. Minor clarifying changes are made and new references added
Scientific paper
10.1016/S0370-2693(98)00315-3
The fixed point Dirac operator on the lattice has exact chiral zero modes on topologically non-trivial gauge field configurations independently whether these configurations are smooth, or coarse. The relation $n_L-n_R = Q^{FP}$, where $n_L$ $(n_R)$ is the number of left (right)-handed zero modes and $Q^{FP}$ is the fixed point topological charge holds not only in the continuum limit, but also at finite cut-off values. The fixed point action, which is determined by classical equations, is local, has no doublers and complies with the no-go theorems by being chirally non-symmetric. The index theorem is reproduced exactly, nevertheless. In addition, the fixed point Dirac operator has no small real eigenvalues except those at zero, i.e. there are no 'exceptional configurations'.
Hasenfratz Peter
Laliena Victor
Niedermayer Ferenc
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