S-duality in Supersymmetric Gauge Theory and String Theory

超对称规范理论和弦理论中的 S 对偶性

• 批准号: 08640353
• 负责人: EGUCHI Tohru
• 金额: $ 1.15万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1996
• 资助国家: 日本
• 起止时间: 1996 至 1997
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08640353/
• 关键词: 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

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_nL_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.

1996年，Eguchi从N=2超对称规范理论的Seiberg-Witten精确解出发，构造了一大类4维超共形场理论，并将其参数调整到临界值。然后，他根据它们的临界指数对这些共形理论进行了分类，并证明了分类遵循A-D-E李代数的模式。1997年Eguchi研究了任意Kahler流形M上的拓扑弦振幅，并证明了它们被无数个微分算子L_nL_nZ=0, n=-1,0,1,2，····(1)湮灭，并且这些算子形成了一个Virasoro代数[L_n， L_m]= (n- M) L_<n+ M >+(X (M))/ (n^3-n) δ _<n+ M，其中X (M)为M的欧拉数。通过用自由场表示Virasoro算子，他进一步证明了拓扑弦的振幅可以用bL_<偶数>自由玻色子和bL_<edd>自由费米子来描述。其中b_<**> (M)为M的贝蒂数。

项目成果

T.Eguchi,K.Hori,K.Ito,S.K.Yang: "Study of N=2 Superconformal Field Theories in S4S Dimensions" Nucl.Phys.B471. 430-442 (1996)

T.Eguchi、K.Hori、K.Ito、S.K.Yang：“S4S 维度中 N=2 超共形场论的研究”Nucl.Phys.B471。

T.Eguchi,S.K.Yang: "Prepotentials in Supersymmetric Gauge Theories and Solition Equations" Mod. Phys.lett.A11 1995. 131-135 (1995)

T.Eguchi，S.K.Yang：“超对称规范理论和孤子方程中的预势”Mod。

T.Eguchi: "Study of N=2 Superconformal Field Thearies in 4 Dimensions." Nucl.Phys.B. 471. 430-444 (1996)

T.Eguchi：“4 维 N=2 超共形场论的研究。”

T.Eguchi: "Study of N=2 Superconformal Field Theories in 4 Dimensions" Nucl.Phys.B. 471. 430-444 (1996)

T.Eguchi：“4 维 N=2 超共形场论的研究”Nucl.Phys.B。

T.Eguchi: "Prepotentials of N=2 Supersymmetric Gauge Theories and Soliton Equations" Mod.Phys.Lett.A. 11. 131-138 (1996)

T.Eguchi：“N=2 超对称规范理论和孤子方程的预势” Mod.Phys.Lett.A。