| Project/Area Number |
09640335
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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 | University of Tsukuba |
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Principal Investigator |
YANG Sung-kil University of Tsukuba, Institute of Physics, Professor, 物理学系, 教授 (70201118)
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| Project Period (FY) |
1997 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥2,300,000 (Direct Cost: ¥2,300,000)
Fiscal Year 1999: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1998: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1997: ¥1,100,000 (Direct Cost: ¥1,100,000)
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| Keywords | supersymmetry / gauge theory / Seiberg-Witten theory / topological field theory / ADE singularity / D-brane / Seibery-Witten理論 / 7-ブレーン / ストリング接合 / 厳密解 / M理論 |
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| Research Abstract |
1. Studying the low-energy effective action of four-dimensional N = 2 supersymmetric gauge theory in the Coulomb branch, we find an intimate relation between the Seiberg-Witten theory and the ADE simple singularity theory. Given spectral curves of the periodic Toda system as Seiberg-Witten curves, we calculate the instanton corrections in the low-energy effective potential. The result is in agreement with that obtained by the microscopic instanton calculus. Our results imply a deep relevance of two-dimensional topological gravity to four-dimensional Seiberg-Witten theory.
2. Considering four-dimensional N = 1 supersymmetric gauge theory with the ADE gauge group coupled to adjoint matters, we derive the low-energy effective superpotential in the confining phase of U (1) photon. As a result, we obtain the complex curves for N = 2 gauge theories and propose the Seiberg-Witten geometry for N = 2 EィイD26ィエD2 gauge theory with massive fundamental hypermultiplets. The relevant manifold is described as a fibration of the ALE space of EィイD26ィエD2 type. Then we determine the Seiberg-Witten geometry for N = 2 SO and SU theory with massive spinor and vector matters by breaking the gauge symmetry of N = 2 EィイD26ィエD2 theory with massive fundamental matters.
3. We study mass deformations of N = 2 superconformal theories with ADE global symmetries on a D3-brane in detail. As an extension of this work, elliptic curves for the IIB 7-brane configurations realizing the E-type affine Lie algebras are systematically derived from the cubic equation for a rational elliptic surface. Moreover, we analyze the structure of singularities, Mordell-Weil lattices and torsions of a rational elliptic surface using string junctions in the background of 12 IIB 7-branes, and find complete agreement with the classification of the Mordell-Weil lattices.
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