| Project/Area Number |
08640353
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
素粒子・核・宇宙線
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| Research Institution | The University of Tokyo |
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Principal Investigator |
EGUCHI Tohru The University of Tokyo, graduate school of science, Professor, 大学院・理学系研究科, 教授 (20151970)
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| Project Period (FY) |
1996 – 1997
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| Project Status |
Completed (Fiscal Year 1997)
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| Budget Amount *help |
¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 1997: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1996: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | supersymmetry / conformal theory / topological field theory / Virasoro algebra / A-D-E classification / 弦理論 / インスタントン / 量子コホモロジー / 特異点 / 臨界指数 / スーパーポテンシャル |
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| Research Abstract |
In the year 1996 Eguchi constructed a large class of 4 dimensional superconformal field theories starting from the Seiberg-Witten exact solutions of N=2 supersymmertic gauge theories and adjusting their parameters to critical values. He then classified these conformal theories based on their critical exponents and has shown that the classification follows after the pattern of the A-D-E Lie algebra.
In the year 1997 Eguchi studied the topological string amplitudes on arbitrary Kahler manifolds M and has shown that they are annihilated by an infinite number of differential operators L_n
L_nZ=0, n=-1,0,1,2, ・・・ (1)
and these operators form a Virasoro algebra
[L_n, L_m]= (n-m) L_<n+m>+(X (M) )/ (n^3-n) delta_<n+m, 0> (2)
Here X (M) is the Euler number of M.By representing the Virasoro operators in terms of free fields he further showed that the topological string amplitudes are described by bL_<even> free bosons and bL_<edd> free fermions. Here b_<**> (M) are the Betti numbers of M.
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