Unification Theories Including Gravity and its Mathematical Structure
Project/Area Number 
02044015

Research Category 
GrantinAid for international Scientific Research

Allocation Type  Singleyear Grants 
Section  Joint Research 
Research Institution  Tohoku University 
Principal Investigator 
OKADA Yasuhiro Tohoku University, Faculty of Science, 理学部, 助手 (20212334)

CoInvestigator(Kenkyūbuntansha) 
FRAMPTON Paul H. University of North Carolina at Chapel Hill, Department of Physics and Astronomy, 物理学及び天文学科, 教授

Project Period (FY) 
1990

Project Status 
Completed (Fiscal Year 1990)

Budget Amount *help 
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1990: ¥2,000,000 (Direct Cost: ¥2,000,000)

Keywords  String theory / Gravity / Padic number / Unification theory / Quark mass matrix / Flavor mixing 
Research Abstract 
In this program we studied two subjects, namely the padic approach to the string theory and the unified theories of the standard and beyond standard models. Supersrting is the most prominent unified theory including gravity. Although many interesting things have been found, the important questions like what is the vacuum structure of string rely on the ability of nonperturbative calculation in string theory. The padic string was initiated to understand new mathematical structure of string in terms of an infinite product formula of the string tree amplitude. This year we reconsidered the padic string amplitude based on BruhatTits tree which is a natural analogy to the world sheet of the ordinary string. We can formulate the padic loop amplitude using this idea. The remaining problems include to clarify the relationship between the padic and ordinarystring theories and to find possible applications of field theories defined over BruhatTits tree. As for unification theories, Frampton and Okada consider the problem of quark masses and flavor mixings. In the standard model with three generations, we have 10 free parameters in the quark sector. Any relations among these parameters suggest physics beyond the standard model. We start a simple ansatz for the quark mass matrices and derive a new relation among two elements of KobayashiMaskawa matrix and up, charmand topquark masses. Once the top quark mass is known and more precise measurements of Bmeson decay are done we can check the validity of the proposed relation. With T. Yanagida, Frampton also studied the strong CP problem in a model with an extra gauge symmetry and heavy fermions called sark. They pointed out that in the sark model with PecceiQuinn symmetry a light axion can be avoided.

Report
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Research Products
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