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Prog. Theor. Phys. Vol. 116 No. 1 (2006) pp. 197-215

[ Full Text PDF : FREE ACCESS (216K) ]

Overlap Lattice Fermion in a Gravitational Field

Masashi Hayakawa,1,* Hiroto So2,** and Hiroshi Suzuki3,***

1,3Theoretical Physics Laboratory, RIKEN, Wako 351-0198, Japan
2Department of Physics, Niigata University, Niigata 950-2181, Japan

(Received April 25, 2005)

Abstract:

We construct a lattice Dirac operator of overlap type that describes the propagation of a Dirac fermion in an external gravitational field. The local Lorentz symmetry is manifestly realized as a lattice gauge symmetry, while it is believed that the general coordinate invariance is restored only in the continuum limit. Our doubler-free Dirac operator satisfies the conventional Ginsparg-Wilson relation and possesses γ5 hermiticity with respect to the inner product, which is suggested by the general coordinate invariance. The lattice index theorem in the presence of a gravitational field holds, and the classical continuum limit of the index density reproduces the Dirac genus. Reduction to a single Majorana fermion is possible for 8k + 2 and 8k + 4 dimensions, but not for 8k dimensions, which is consistent with the existence of the global gravitational/gauge anomalies in 8k dimensions. Other Lorentz representations, such as the spinor-vector and the bi-spinor representations, can also be treated. Matter fields with a definite chirality (with respect to the lattice-modified chiral matrix) are briefly considered.


URL : http://ptp.ipap.jp/link?PTP/116/197/
DOI : 10.1143/PTP.116.197


*E-mail: haya@riken.jp
**E-mail: so@muse.sc.niigata-u.ac.jp
***E-mail: hsuzuki@riken.jp

[ Full Text PDF : FREE ACCESS (216K) ] Citation:

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