Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2006-04-04
Prog.Theor.Phys. 116 (2006) 197-215
Physics
High Energy Physics
High Energy Physics - Lattice
22 pages, uses PTPTeX.cls, the final version to appear in Prog. Theor. Phys
Scientific paper
10.1143/PTP.116.197
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 gamma_5 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.
Hayakawa Masashi
So Hiroto
Suzuki Hiroshi
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