1998 Fiscal Year Final Research Report Summary
Differential equations for periods and super string and susy gauge theories
| Project/Area Number |
09440021
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (B)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | KOBE UNIVERSITY |
|---|
Principal Investigator |
YAMADA Yasuhiko Kobe University Graduate school of Natural Science Associate Professor, 大学院・自然科学研究科, 助教授 (00202383)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
YANG Sung-Kil Tsukuba University Faculty of Science Professor, 物理学系, 教授 (70201118)
HOSONO Shinobu Tokyo University Faculty of Science Associate Professor, 大学院・数理科学科, 助教授 (60212198)
|
|---|
| Project Period (FY) |
1997 – 1998
|
| Keywords | Super symmetry / Seiberg-Witten theory / Period integrals / String thory / Mirror symmetry / Integrability / Painleve equation / Topological field theory |
|---|
| Research Abstract |
In this project, each of the three investigators carried out his research independently with in close co-operation. Inspiring with each other, we can obtain successful results more than our initial aim.
1. Y.Yamada studied the relation between the integrable structure in the two dimensional quantum gravity and singularity theories. He found deep connections between the KP equations, Drinfeld-Sokolov equations and Painleve equations, and obtained successful results on the theory of Painleve equations and their symmetries. This result is expected to be applied to other problems in mathematical physics.
2. S.K.Yang investigated the Seiberg-Witten curves (or more general geometries) in N = 2 susy gauge theories in systematic way with explicit examples. He clarify the profound relation with the singularity theories and determine the geometrical structures for exceptional gauge groups.
3. S.Hosono has continued the research on the mirror symmetry. He made important contribution for the evaluation of the Gromov-Witten invariants for elliptic- or K3-fibered Calabi-Yau manifolds. There is also some progress in counting the higher genus curves from theoretical and computing points of view.
|
