Topological Field Theory Coupled with 2D Quantum Gravity
Grant-in-Aid for Scientific Research (C)
|Allocation Type||Single-year Grants|
|Research Institution||Shizuoka University|
AOYAMA Shogo Shizuoka University, Physics, Professor, 理学部, 教授 (10273161)
|Project Period (FY)
1996 – 1997
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|
Continuing the research project in 1996, I tried to phenomelogically understand the Seiberg-Witten solution of quantum chromo dynamics (QCD) by means of a two-dimensional 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 Landau-Ginzburg 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 six-dimensional representation :
The moduli of QCD vacuum is described by a topological field theory with a Landau-Ginzburg potential which is a polynomial of the third degree.
2. The eigth-dimensional representation :
This case is also described by a topological field theory, but its Landaw-Ginzburg potential is irrational function with branch-cuts. 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 ten-dimnsional representation :
The Landau-Ginzburg 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 Landau-Ginzburg 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 two-dimensional topological field theory can be described by two different Lndaw-Ginzburg potential.
Research Output (1results)