Duality and modular form in topological gauge theory
Project/Area Number  10640081 
Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Geometry

Research Institution  Hiroshima University 
Principal Investigator 
KANNO Hiroaki Hiroshima Univ., Faculty of Science, Associate Professor, 理学部, 助教授 (90211870)

Project Period (FY) 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥2,800,000 (Direct Cost : ¥2,800,000)
Fiscal Year 1999 : ¥1,100,000 (Direct Cost : ¥1,100,000)
Fiscal Year 1998 : ¥1,700,000 (Direct Cost : ¥1,700,000)

Keywords  Instanton / Topological gauge theory / Special holonomy group / Supersymmetric cycle / 超対称ゲージ理論 / 位相的場の量子論 / SeibergWitten 理論 
Research Abstract 
From the viewpoint of nonperturbative dynamics of supersymmetric gauge theory and dualities of superstring theory we have investigated the geometry of instanton moduli space in higher dimensions and its relation to supersymmetric cycles, which are naturally introduced on the manifold of special holonomy. We first argued that supersyrnmetric cycles play a significant role in the problem of compactifying the instanton moduli space in higher dimensions. As an explicit example we constructed the octonionic instanton solutions on a noncompact eightdimensional manifold with Spin (7) holonomy. However, our understanding of the geometry of its moduli space is still incomplete and it is an open problem to construct a new kind of topological invariants based on the octonionic instanton moduli space. Quite recently a substantial progress has been made in the five dimensional supersymmetric gauge theory compactified on a circle, which was the research subject in 1998. It seems possible to understand the spacetime instanton in topological gauge theory from the worldsheet instanton of string theory in which the mirror symmetry gives a powerful tool.

Report
(3results)
Research Products
(8results)