2006 Fiscal Year Final Research Report Summary
Analysis of algebraic and geometrical structure in superstring theory
| Project/Area Number |
13135212
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| Research Category |
Grant-in-Aid for Scientific Research on Priority Areas
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| Allocation Type | Single-year Grants |
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| Review Section |
Science and Engineering
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| Research Institution | Utsunomiya University (2006)
Nagoya University (2001-2005) |
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Principal Investigator |
UEHARA Shozo Utsunomiya University, Faculty of Engineering, Professor (20168652)
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| Co-Investigator(Kenkyū-buntansha) |
AOYAMA Shogo Shizuoka University, Faculty of Science, Professor (10273161)
KAWAI Toshiya Kyoto University, Research Institute for Mathematical Sciences, Associate Professor (20293970)
AWATA Hidetoshi Nagoya University, Graduate School of Mathematics, Associate Professor (40314059)
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| Project Period (FY) |
2001 – 2006
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| Keywords | M-theory / supermembrane / superstring / Kaehler manifolds / Calabi-Yau manifolds / Gromov-Witten invariants / Gopakumar-Vafa invariants / Nekrasov's formula |
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| Research Abstract |
In this project, the head investigator S. Uehara investigated the supermembrane theory which is one of the important fundamental excitations of M-theory. Uehara succeeded in giving the matrix representation of the affine Lie algebra which appears when supermembrane wraps on a circle. Uehara also gave the matrix representation of the wrapped supermembrane on 2-torus. Furthermore, Uehara succeeded in deriving the(p, q)-string action directly from the supermembrane action.
S. Aoyama showed a new formula of the triplet Killing potentials of quatenionic Kaehler manifolds with the metric of the manifolds. Aoyama also investigated two-dimensional non-linear sigma-models on the Kaehler maniforld G/H in the first order formalism and constructed the G-symmetry currents and primaries by using the Berkovits method.
T. Kawai discussed the geometry of D2-D0 branes may be related to Gromov-Witten theory of Calabi-Yau threefolds. Kawai also discussed the relation to Gopakumar-Vafa invariants.
H. Awata investigated the connection of Nekrasov's partition function in the Omega background and the moduli space of D-branes and showed that the spin contents obtained by Nekrasov's formula are consistent with the Gopakumar-Vafa invariants on a local Hirzebruch surface. Awata also proposed the refined topological vertex in terms of the specialization of the Macdonald function.
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