Index of a family of lattice Dirac operators and its relation to the non-abelian anomaly on the lattice
Adams, David H.
Date of Issue2001
School of Physical and Mathematical Sciences
In the continuum, a topological obstruction to the vanishing of the non-Abelian anomaly in 2n dimensions is given by the index of a certain Dirac operator in 2n+2 dimensions, or equivalently, the index of a 2-parameter family of Dirac operators in 2n dimensions. In this paper an analogous result is derived for chiral fermions on the lattice in the overlap formulation. This involves deriving an index theorem for a family of lattice Dirac operators satisfying the Ginsparg-Wilson relation. The index density is proportional to Lüscher's topological field in 2n+2 dimensions.
Physical and Mathematical Sciences
Physical review letters
© 2001 The American Physical Society. This paper was published in Physical Review Letters and is made available as an electronic reprint (preprint) with permission of The American Physical Society. The paper can be found at the following official DOI:http://dx.doi.org/10.1103/PhysRevLett.86.200. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.