2007 Fiscal Year Final Research Report Summary
Non-perturbative construction of non-abelian chiral gauge theories on four and two-dimensional lattice and numerical applications
| Project/Area Number |
17540249
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Particle/Nuclear/Cosmic ray/Astro physics
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| Research Institution | The University of Tokyo (2006-2007)
Nagoya University (2005) |
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Principal Investigator |
KIKUKAWA Yoshio The University of Tokyo, Graduate school of Arts and Sciences, Associate Professor (20252421)
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| Project Period (FY) |
2005 – 2007
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| Keywords | Quantum Field Theory / Lattice Gauge Theory / chiral symmetry / Gauge anomaly / chiral gauge theory / Weinberg-Salam model |
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| Research Abstract |
Non-abelian chiral gauge theory posseses several interesting dynamical possibilities such as spontaneous gauge symmetry breaking, appearance of composite massless fermions, generation of fermion number asymmetry due to chiral anomaly and so on. These dynamical properties may be useful to build the model of elementary particles beyond the standard model. The purpose of this research is to construct chiral gauge theories non-perturbatively and to study dynamical aspects of these theories in the framework of lattice field theory.
In lattice gauge theory, to keep gauge invariance, one must establish the exact cancellation of gauge anomalies among chiral fermions, not only in the continuum limit, but also at finite lattice spacing. To achieve this, it is necessary to find a solution to so-called local cohomology problem. So far, only in U(1) theories, a solution has been known.
In our study, we have given a solution to the local cohomology problem in SU(2) x U(1) theory. Furthermore, we have given a non-perturbative formulation of the Glashow-Weinberg-Salam model (the Electroweak theory) on the lattice with exact gauge invariance. Our construction covers all SU(2) topological sectors with vanishing magnetic fluxes. Therefore it may be usable to describe the fermion number non-conservation in the early universe.
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Research Products
(8 results)
