2006 Fiscal Year Final Research Report Summary
Non-perturbative renormalization group approach to supersymmetric nonlinear sigma models
| Project/Area Number |
16340075
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Osaka University |
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Principal Investigator |
HIGASHIJIMA Kiyoshi Osaka University, Graduate School of Science, Professor (10092313)
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| Project Period (FY) |
2004 – 2006
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| Keywords | Renormalization Group / Nonlinear sigma model / Ricci flow / Einstein-Kaehler manifold / Three dimensional sigma model / Supersymmetric sigma model |
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| Research Abstract |
1. The Wilsonian renormalization group equation for three dimensional nonlinear sigma models was derived.
2. Conformal invariant field theories are defined as the fixed point theory of that equation. Nonlinear sigma models on Einstein-Kahler manifolds correspond to ultraviolet fixed points.
3. We have analyzed conformal field theories in details when the target manifold has real dimensions two.
(1) When the anomalous dimension γ=-1/2, the target manifold is a round two sphere with enhanced symmetry SU (2).
(2) When -1/2<γ<0, the target manifold is compact but has conical singularity.
(3) When γ=0, the target manifold becomes flat corresponding to a free field theory.
(4) The target manifold becomes noncompact when γ>0.
4. When γ=-1/2, we have studied the renormalization group flow of the fluctuations around the round sphere, and found all fluctuations are irrelevant in the infrared region, that is, the shape of the target manifold becomes round shaped in the infrared region.
5. In Wilsonian renormalization method, renormalizability is equivalent to the existence of ultraviolet fixed point such that we can take the nontrivial continuum limit. To confirm our result, we have also shown that these models are also renormalizable in the large N expansion method.
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