| Budget Amount *help |
¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 2004: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 2003: ¥1,700,000 (Direct Cost: ¥1,700,000)
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| Research Abstract |
(1)It is commonly believed that the large N limit of gauge theories is described by so-called Eguchi-Kawai's reduced model. We considered a reduced model which corresponds to chiral gauge theories on the lattice and systematically studied possible gauge anomalies in this model at the first time. In this study, we presented, for a wide class of gauge field configurations, a calculational method of anomalies for fermions in the fundamental representation of gauge group U(N). Next, we calculated anomalies in a large N limit for general gauge group representations. (2)In recent years, a formulation of chiral gauge theories on the lattice on the basis of the Ginsparg-Wilson relation. We formulate, based on this development, the Wess-Zumino-Witten action on the lattice and analyzed geometrical properties of the formulation. We found, as a consequence of the use of Ginsparg-Wilson relation, that topological properties of the Wess-Zumino-Witten action are ensured even on the lattice. (3) It ha
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s been known that two-dimensional bosonization can be interpreted by using the anomaly. In this argument, however, a seemingly irrelevant term which may be removed by a local counter term plays a crucial role. There was confusion in the literature on an understanding on this point ; we clarified the origin of this confusion based on the locality argument. (4) We pointed out that there is a fundamental difficulty concerning lattice formulation of the Majorana and Majorana-Weyl fermions, depending on the dimensionality of spacetime. We argued that, this difficulty is closely related to Witten's global gauge anomaly. (5) We reconsidered a quantization of gauge theories with local gauge anomalies from a view point, of a lattice formulation based on the Ginsparg-Wilson relation. We showed that a consistent formulation of such systems is generally impossible. We also argued a possible implication for theories in which the anomaly is cancelled by the Green-Schwarz mechanism. (6) We constructed a lattice formulation of four dimensional supersymmetric Wess-Zumino model which preserves the exact. U(1)R symmetry. Less
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