Grant-in-Aid for Scientific Research on Priority Areas (B)
|Research Institution||University of Tsukuba|
SATOH Yuji Institute of Physics, Assistant Professor, 物理学系, 助手 (50312799)
YANG Sung-kil Institute of Physics, Professor, 物理学系, 教授 (70201118)
NAKATSU Toshio Department of Physics, Graduate School of Science, Osaka University, Assistant Professor, 大学院・理学系研究科, 助手 (10281502)
細野 忍 東京大学, 大学院・理学研究科, 助教授 (60212198)
ITO Katsushi Department of Physics, Faculty of Science, Tokyo Institute of Technology, Associate Professor, 大学院・理工学研究科, 助教授 (60221769)
野口 雅之 筑波大学, 物理学系, 助手 (70292498)
MOHRI Kenji Institute of Physics, Assistant Professor, 物理学系, 助手 (90302348)
OHTA Nobuyoshi Department of Physics, Graduate School of Science, Osaka University, Associate Professor, 大学院・理学系研究科, 助教授 (90167304)
谷口 裕介 筑波大学, 物理学系, 助手 (60322012)
|Project Fiscal Year
1998 – 2001
Completed(Fiscal Year 2001)
|Budget Amount *help
¥8,500,000 (Direct Cost : ¥8,500,000)
Fiscal Year 2001 : ¥1,700,000 (Direct Cost : ¥1,700,000)
Fiscal Year 2000 : ¥1,600,000 (Direct Cost : ¥1,600,000)
Fiscal Year 1999 : ¥2,500,000 (Direct Cost : ¥2,500,000)
Fiscal Year 1998 : ¥2,700,000 (Direct Cost : ¥2,700,000)
|Keywords||supersymmetry / string theory / D-brane / Calbi-Yau manifold / Seiberg-Witten theory / black hole / AdS / CFT correspondence / non-commutative geometry / 超対称性 / 弦理論 / D-ブレイン / カラビ・ヤウ多様体 / Seiberg-Witten理論 / ブラックホール / CFT対応 / 非可換時空 / Dブレイン / カイラルフェルミオン / Ads / 位相的場の理論|
The purpose of this research was to study superstring theory and moduli spaces of supersymmetric gauge theories ('superstring geometry') by various mathematical and physical considerations. and verify the superstring duality in quantitative and rigorous manners.
In 1998 (academic year), we derived the WDVV equations for some four-dimensional supersymmetric gauge theories, generalized related Donaldson-Witten invariants, and determined the Seiberg-Witten geometries in the cases with the gauge groups of the exceptional type. A rigorous description of the moduli spaces was also obtained by embedding them into M-theory.
In 1999, we obtained the low-energy effective theories of the four-dimensional supersymmetric gauge theories with the exceptional-type flavor symmetries, and clarified its relation to five-dimensional theories. We also found a systematic method for analyzing D-branes on orbifold singularities of Calabi-Yau manifolds, and the generating function for the number of rational curv
es in rational elliptic surfaces. Moreover, we systematically constructed the superconformal algebras in the AdS/CFT correspondence, which is related to the string duality.
In 2000, we showed the dualities between some string junctions and the D-branes on del Pezzo surfaces in Calabi-Yau manifolds, and analyzed in detail the superconformal algebras related to the degenerated Calabi-Yau manifolds of the ADE type. We also obtained the exact correlation functions of the CFT with the AdS_3 target space and, using the AdS/CFT correspondence, clarified properties of the three-dimensional black hole and field theories on non-commutative geometries.
In 2001, we found the prepotentials and Seiberg-Witten curves for the four-dimensional compactified models obtained from the six-dimensional non-critical string theory with the E_8 symmetry. We also derived rigorous properties about the operator product expansion for the AdS_3 CFT and the soliton scattering on non-commutative geometries.
In this way, we obtained many useful and rigorous results about the superstring geometry and the string duality. Less