%0 Journal Article %1 Hasenfratz:1998ri %A Hasenfratz, Peter %A Laliena, Victor %A Niedermayer, Ferenc %D 1998 %J Phys. Lett. %K ChiralSymmetry IndexTheorem Lattice Locality PerfectAction QCD %P 125-131 %R 10.1016/S0370-2693(98)00315-3 %T The index theorem in QCD with a finite cut-off %U http://www.slac.stanford.edu/spires/find/hep/www?eprint=hep-lat/9801021 %V B427 %X Abstract: 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'.

@article{Hasenfratz:1998ri, abstract = { Abstract: 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'. }, added-at = {2009-03-05T17:31:58.000+0100}, archiveprefix = {arXiv}, author = {Hasenfratz, Peter and Laliena, Victor and Niedermayer, Ferenc}, biburl = {https://www.bibsonomy.org/bibtex/2d4055f4cc48c0443426ddb16931fedbe/gber}, description = {SPIRES-HEP: FIND EPRINT HEP-LAT/9801021}, doi = {10.1016/S0370-2693(98)00315-3}, eprint = {hep-lat/9801021}, interhash = {fcdb953db7d50725cfdc8dd7ec9419a6}, intrahash = {d4055f4cc48c0443426ddb16931fedbe}, journal = {Phys. Lett.}, keywords = {ChiralSymmetry IndexTheorem Lattice Locality PerfectAction QCD}, pages = {125-131}, slaccitation = {%%CITATION = HEP-LAT/9801021;%%}, timestamp = {2009-03-11T17:32:52.000+0100}, title = {{The index theorem in QCD with a finite cut-off}}, url = {http://www.slac.stanford.edu/spires/find/hep/www?eprint=hep-lat/9801021}, volume = {B427}, year = 1998 }