Topological Field Theory Coupled with 2D Quantum Gravity
Project/Area Number  08640364 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
素粒子・核・宇宙線

Research Institution  Shizuoka University 
Principal Investigator 
AOYAMA Shogo Shizuoka University, Physics, Professor, 理学部, 教授 (10273161)

Project Fiscal Year 
1996 – 1997

Project Status 
Completed(Fiscal Year 1997)

Budget Amount *help 
¥2,000,000 (Direct Cost : ¥2,000,000)
Fiscal Year 1997 : ¥1,000,000 (Direct Cost : ¥1,000,000)
Fiscal Year 1996 : ¥1,000,000 (Direct Cost : ¥1,000,000)

Keywords  Prticle Theory / 2D Quantum Gravity / topological field theory / 素粒子論 / 2次元量子重力 / 位相的場の理論 
Research Abstract 
Continuing the research project in 1996, I tried to phenomelogically understand the SeibergWitten solution of quantum chromo dynamics (QCD) by means of a twodimensional topological field theory. Namely I expected that moduli of QCD vacuum depend on the renormalization group flow and satisfy a kind of renormalization group equation. I conjectured that sucth a renormalization group equation has an integrable structure and the moduli of QCD vacuum could be described by a two dimensional topological field theory with a LandauGinzburg potential. I concretely checked this conjecture by computer calculation. The results for the gauge group SU (3) are given below, depending on the representation of Higgs fields. 1. The fundamental or sixdimensional representation : The moduli of QCD vacuum is described by a topological field theory with a LandauGinzburg potential which is a polynomial of the third degree. 2. The eigthdimensional representation : This case is also described by a topological field theory, but its LandawGinzburg potential is irrational function with branchcuts. One should remark that the fusion algebra is the same as in the case 1 and therefore the topological field theory with this potential is equivalent to the one discussed in the case 1.However it is an important future subject to know an equation to determine the renormalization group flow. 3. The tendimnsional representation : The LandauGinzburg potentail in this case is the same as obtained in the case 1 or the case 2. One may expect the similar phenomena of the LandauGinzburg potential even in higher dimensional representation of the Higgs fields. I emphasize that the result in the case 2 in important in the sense that a twodimensional topological field theory can be described by two different LndawGinzburg potential.

Report
(4results)
Research Output
(1results)