2001 Fiscal Year Final Research Report Summary
Studies of Lattice Garuge Models with θ-Term by Numerical Simulations and Renormalization Group Method
| Project/Area Number |
11640248
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
素粒子・核・宇宙線
|
|---|
| Research Institution | YANAGATA UNIVERSITY |
|---|
Principal Investigator |
IMACHI Gasahiro Yamagata University, Department of Physics, Professor, 理学部, 教授 (70037208)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
YONEYAMA Hiroshi Saga University, Department of Physics, Professor, 理工学部, 教授 (50210795)
|
|---|
| Project Period (FY) |
1999 – 2001
|
| Keywords | Lattice gauge theory / CP^<N-1> model / θ-term / topological charge distribution / strong CP violation / first order phase transition / confinement / fixed point action |
|---|
| Research Abstract |
Much progress was done in understanding of non-perturbative aspect of gauge theories by lattice gauge theory approach. Studies up to now were mainly about the systems without θ-term, i.e., topological term. The role of θ-term is not known well. Two dimensional CP^<N-1> model and four dimensional QCD have many common properties. Schierholz suggested the value of θ will go to zero in continuum limit. If it is true the problem of Strong CP violation is reduced to the dynamical property of the gauge system itself. When the system has θ-term, numerical simulation will be difficult because the Boltzmann factor becomes complex number and cannot be used as the probability weight. The aim of this project is to develop the method to perform numerical simulations about the system with θ-term. Topological charge distribution P(Q) is obtained with real positive Boltzmann weight without θ-term. Then the partition function is obtained by the Fourier series with weight exp(iθQ/2π). We found free energy shows "flattening" at some value of θ. The origin of this flattening, in our investigation, is due to the statistical error in P(Q = 0) but not due to the first order phase transition (this latter interpretation is made by Schieholz). We also studied the system based on "fixed point action", which is expected to be closer to continuum limit. Scaling behavior is found in CP^3 but not in CP^1 model. We are now studying Z_N lattice gauge theory by real space renormalization group approach to investigate "oblique confinement" which is expected by Cardy- Rabinovici using free energy argument.
|
