Solvable Iattice models associated with supera I gebras and related topics
Project/Area Number |
19740244
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Single-year Grants |
Research Field |
Mathematical physics/Fundamental condensed matter physics
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Research Institution | Okayama Institute for Quantum Physics |
Principal Investigator |
TSUBOI Zengo Okayama Institute for Quantum Physics, 協力研究員 (90416420)
TSUBOI Zengo (2009) Okayama Institute for Quantum Physics, 岡山光量子科学研究所, 研究員 (19740244)
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Project Period (FY) |
2007 – 2010
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Project Status |
Completed (Fiscal Year 2010)
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Budget Amount *help |
¥3,730,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥1,000,000 (Direct Cost: ¥1,000,000)
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Keywords | 数理物理 / 可解模型 / ベーテ仮説 / AdS / CFT対応 / superalgebra / 表現論 / 統計力学 / 可積分系 / AdS/CFT対応 / ソリトン / べーテ仮説 / 表現諭 / ベーテ仮説法 / Baxter Q-operator / q-supercharacter / 可解格子膜型 / Baxter Q演算子 |
Research Abstract |
We have researched on the following topics on integrable models related to superalgebras. We have constructed the Baxter Q-operators for Uq(sl(2 11)1), functional relations among them and Wronskian-type expressions of T-operators (transfer matrices). Our formulation can be applicable to both lattice models and conformal field theory since it is independent of the space where the operators act on. I made non-trivial generalization of Wronskian-type formulae to Uq(gl(M I N)A) case, and gave Wronskian-type solutions of the T-system. They are yet another form of the so-called q-(super)characters. I identified that the number of the Baxter Q-operators is 2A{M+N} for the first time. Based on the technique developed through the above research, we gave solutions to the T-and Q-systems for the AdS/CFT in particle physics. We proposed a new definition of the 2A{M+N} Baxter Q-operators based on 'co-derivative' on generating functions of supercharacters of gl(M I N), and derived the Bethe ansatz equations without using the Bethe ansatz. We also clarified relations between Backlund transformations in the soliton theory and the Baxter Q-operators on the level of operator.
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Report
(6 results)
Research Products
(46 results)
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[Presentation] Baxter Q-operators for U_{q}(sl(2|1))2007
Author(s)
Zengo Tsuboi
Organizer
La 79eme Rencontre entre physiciens theoriciens et mathematiciensSupersymmetry and Integrability"
Place of Presentation
Institut de Recherche Mathematique Avancee (IRMA), Strasbourg.
Year and Date
2007-06-02
Related Report
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[Presentation] Baxter Q-operators for U_{q}(sl(2|1))2007
Author(s)
Zengo Tsuboi
Organizer
La 79eme Rencontre entre physiciens theoriciens et mathematiciens "Supersymmetry and Integrability"
Place of Presentation
Institut de Recherche Mathematique Avancee (IRMA), Strasbourg
Year and Date
2007-06-02
Related Report
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[Presentation] Baxter Q-operators for U_{q}(hat[sl](2|1))2007
Author(s)
坪井 禅吾
Organizer
La 79eme Rencontre entre physiciens theoricienset mathematiciens"Supersymmetry andIntegrability"
Place of Presentation
Institut de Recherche Mathe matique Avancee(IRMA),Strasbourg,France
Year and Date
2007-06-02
Related Report
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