2005 Fiscal Year Final Research Report Summary
Algebraic study of integrable systems coming from field theories
| Project/Area Number |
15540014
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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 |
Algebra
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| Research Institution | Ochanomizu University |
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Principal Investigator |
TAKEBE Takashi Ochanomizu University, Department of Mathematics, Associate Professor, 理学部, 助教授 (60240727)
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| Project Period (FY) |
2003 – 2005
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| Keywords | WZW model / elliptic curves / twisted WZW model / orbifold WZW model / Rational Conformal Field Theory / Separation of Variables / Loewner equation |
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| Research Abstract |
I studied the "twisted WZW model", which is a non-standard WZW model on elliptic curves. The factorisation theorem, which states that the sheaf of conformal blocks is locally free even at the boundary of the moduli space where the elliptic curve degenerates to a singular rational curve, has been proved. The sheaf of conformal blocks becomes that of the orbifold WZW model.
In particular, if one inserts integrable representations to marked points on the elliptic curve, this model gives another example of the rational conformal field theory.
I studied the following related topics, too :
1.Construction and generalisation of an integrable system on the monopole moduli space (a space of rational functions). Separation of variables of this system.
2.Relation of the Lowner equations and dispersionless integrable systems, in view of the boundary conformal field theory.
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