Index of a family of lattice Dirac operators and its relation to the non-abelian anomaly on the lattice
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...
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sg-ntu-dr.10356-1011192023-02-28T19:43:11Z Index of a family of lattice Dirac operators and its relation to the non-abelian anomaly on the lattice Adams, David H. School of Physical and Mathematical Sciences 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. Published version 2013-12-16T08:20:43Z 2019-12-06T20:33:36Z 2013-12-16T08:20:43Z 2019-12-06T20:33:36Z 2001 2001 Journal Article Adams, D. H. (2001). Index of a Family of Lattice Dirac Operators and Its Relation to the Non-Abelian Anomaly on the Lattice. Physical Review Letters, 86(2), 200-203. https://hdl.handle.net/10356/101119 http://hdl.handle.net/10220/18276 10.1103/PhysRevLett.86.200 en 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. 4 p. application/pdf |
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Physical and Mathematical Sciences Adams, David H. Index of a family of lattice Dirac operators and its relation to the non-abelian anomaly on the lattice |
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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. |
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School of Physical and Mathematical Sciences |
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School of Physical and Mathematical Sciences Adams, David H. |
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Article |
author |
Adams, David H. |
author_sort |
Adams, David H. |
title |
Index of a family of lattice Dirac operators and its relation to the non-abelian anomaly on the lattice |
title_short |
Index of a family of lattice Dirac operators and its relation to the non-abelian anomaly on the lattice |
title_full |
Index of a family of lattice Dirac operators and its relation to the non-abelian anomaly on the lattice |
title_fullStr |
Index of a family of lattice Dirac operators and its relation to the non-abelian anomaly on the lattice |
title_full_unstemmed |
Index of a family of lattice Dirac operators and its relation to the non-abelian anomaly on the lattice |
title_sort |
index of a family of lattice dirac operators and its relation to the non-abelian anomaly on the lattice |
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2013 |
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https://hdl.handle.net/10356/101119 http://hdl.handle.net/10220/18276 |
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1759855177235431424 |