2003 Fiscal Year Final Research Report Summary
Study of supersymmetric non-linear sigma models
| Project/Area Number |
13640283
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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 |
素粒子・核・宇宙線
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| Research Institution | Osaka University |
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Principal Investigator |
HIGASHIJIMA Kiyoshi Osaka University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (10092313)
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| Project Period (FY) |
2001 – 2003
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| Keywords | Non-linear sigma model / renormalization group / Ricci-flat manifold / auxiliary field formulation / large N method / Einstein-Kahler manifold |
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| Research Abstract |
Study of non-linear sigma models is important for several reasons. Two-dimensional non-linear sigma models describe propagation of strings in vurved space-time. It is also a gymnasium for non-perturbative study of difficult phenomena in field theories, like mass generation, bound states problem, dynamical symmetry breaking. It also offers an example of a possible renormalizable field theory that is not renormalizable in perturbation theory. In this project, we proposed
A)Auxiliary field formulation of non-linear sigma models with N=2 supersymmetry.
B)Non-perturbative study of N=2 supersymmetric non-linear sigma models by using the above method
C)Search of conformal field theories by using the renormalization group equation.
D)Study of conformally invariant non-linear sigma models on non-compact manifolds.
We successfully formulated N=2 supersymmetric non-linear sigma models on hermitian symmetric spaces by introducing both D-term and F-term constraints. We applied the large N method to study the non-perturbative phenomena in non-linear sigma models on CP^N and Q^N. We also obtained conformal field theories on non-compact Ricci-flat manifolds constructed as a line bundle Einstein-Kahler manifold. We derived the non-perturbative renormalization group equation for N=2 supersymmetric non-linear sigma models. By solving the fixed point equation, we found new conformal field theories with anomalous dimension.
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