| DATE: |
2006-06-27 11:00 - 12:00 |
| PLACE: |
Kenkyu Honkan 2F RM 220 |
| TITLE: |
Overlap lattice fermion in a gravitational field |
| CONTACT: |
tsuda |
| SPEAKER: |
Hiroshi Suzuki (RIKEN) |
| LANGUAGE: |
Japanese |
| ABSTRACT: |
We construct a lattice Dirac operator of the overlap-type which describes the propagation of the Dirac fermion in an external gravitational field. The local Lorentz symmetry is manifestly realized as a lattice gauge symmetry, while the general coordinate invariance is expected to be restored only in the continuum limit. Our doubler-free Dirac operator obeys the conventional Ginsparg-Wilson relation and possesses a $\gamma_5$ hermiticity with respect to the inner product which is suggested from 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 as being consistent with the existence of the global gravitational/gauge anomalies in the latter dimensions. Other Lorentz representations, such as the spinor-vector and the bi-spinor representations, can also be treated. Matter fields with a definite chirality is briefly considered.
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