Application of string theory to localization problem
Project/Area Number  04452048 
Research Category 
GrantinAid for Scientific Research (B).

Research Field 
物理学一般

Research Institution  University of Tokyo 
Principal Investigator 
HIKAMI Shinobu University of Tokyo, College of Arts and Sciences, Professor, 教養学部, 教授 (30093298)

Project Fiscal Year 
1992 – 1993

Project Status 
Completed(Fiscal Year 1993)

Budget Amount *help 
¥700,000 (Direct Cost : ¥700,000)
Fiscal Year 1993 : ¥700,000 (Direct Cost : ¥700,000)

Keywords  String theory / Anderson localization / Two dimensional gravity / Matrix model / Quantum Hall effect / ストリング理論 / アンダーソン局在 / 二次元重力 / マトリックス模型 / 量子ホール効果 / 弦理論 / 二次元量子重力 / イジング模型 
Research Abstract 
Anderson localization has been studied by field theoretical method. In this research, the relation to string theory is investigated and by the use of the string scattering amplitude, the renormalization group equation for the Anderson localization is determined up to fiveloop order. The multimoment of conductivity fluctuation is also shown to be related to the dilaton and the massive field renormalizations. The string theory is closely related to the twodimensional gravity coupled to matter fields. Matrix model for such case is investigated especially for the central charge c greater than one. The string susceptibility is evaluated from the perturbative series expansion. In a strong magnetic field, two dimensional electron within the lowest Landau level shows the quantum Hall effect. In a twosubband model, the state at the band center is shown to be delocalized and the exact value of the conductivity is obtained. Two dimensional electron in a strong magnetic field is described by Laughlin wave function. Using a complex matrix, which represents the two dimensional coordinate of electrons, we evaluate the correlation function at the edge state and confirmed the result of the conformal field theory. Also the relation to the two dimensional gravity is investigated by adding the interaction term.

Report
(4results)
Research Output
(20results)