Understanding of random matrix theory from topological field theoryand its applications

• Project/Area Number: 19540395
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: The University of Tokyo
• Principal Investigator: HIKAMI Shinobu The University of Tokyo, 大学院・総合文化研究科, 教授 (30093298)
• Project Period (FY): 2007 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000); Fiscal Year 2008: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2007: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: 数理物理 / メゾスコピック系 / リーマン面 / トポロジー / 統計力学 / 物性理論 / ランダム行列

Research Abstract

外場があるランダム行列模型での密度相関関数のフーリエ変換が点付きモジュライ空間のスピン曲線の交点数を与える導出関数になっていることを双対定理とレプリカ法により示した。レプリカ法により点付きモジュライ空間の曲線のトポロジカルな意味が明瞭になり、また双対定理により外場があるランダム行列模型がギャップをもつ相転移点でのスケーリング則との関係も明らかにすることが出来た。Witten 予想を具体的に相関関数の積分表示で書き、それが一般化されたKontsevich マトリックス模型と等価であることから証明することが出来た。

Research Products

• [Journal Article] Computing topological invariants with one and two-matrix models (2009)
  • Author(s): E.Brezin and S.Hikami
  • Journal Title: JHEP 04 Pages: 110-110
• [Journal Article] Intersection theory from dualityand replica (2008)
  • Author(s): E.Brezin and S.Hikami
  • Journal Title: Commun. math. Phys 283 Pages: 507-507
• [Journal Article] Intersection numbersfrom the antisymmetric Gaussian matrix model (2008)
  • Author(s): E.Brezin and S.Hikami
  • Journal Title: JHEP 07 Pages: 50-50
• [Journal Article] Intensecton numbers from the antisymmetric Gaussian matrix model (2008)
  • Author(s): E. Brezin and S. Hikawi
  • Journal Title: Journal of High Enengy Physics 07 Pages: 50-50
  • Peer Reviewed
• [Journal Article] Intensecton Theory from Duality and Replica (2008)
  • Author(s): E. Brezin and S. Hikawi
  • Journal Title: Communications in Mathematical physics 283 Pages: 507-521
  • Peer Reviewed
• [Journal Article] Intersection Theory from Duality and Replica (2008)
  • Author(s): E. Brezin, S. Hikami
  • Journal Title: Communications in Mathematical Physics 283 Pages: 507-521
  • Peer Reviewed
• [Journal Article] Intersection numbers of Riemann surfaces from Gaussian matrix models (2007)
  • Author(s): E.Brezin and S.Hikami
  • Journal Title: JHEP 10 Pages: 96-96
• [Journal Article] Vertices from replica (2007)
  • Author(s): E.Brezin and S.Hikami
  • Journal Title: J. Phys A.40 Pages: 13545-13545
• [Journal Article] Instanton and superconductivity in supersymmetric CP(N-1)model (2007)
  • Author(s): S.Hikami and T.Yoshimoto
  • Journal Title: J. Phys A.40
• [Journal Article] Vertices from replica in a random matrix theory (2007)
  • Author(s): E. Brezin, S. Hikami
  • Journal Title: Journal of Physics A 40 Pages: 13545-13566
  • Peer Reviewed
• [Journal Article] Intersection numbers of Riemann surfaces from Gaussian matrix models (2007)
  • Author(s): E. Brezin, S. Hikami
  • Journal Title: Journal of High Energy Physics 10 Pages: 96-96
  • Peer Reviewed
• [Presentation] Intensecton Theory from Duality and Replica (2009)
  • Author(s): S. Hikawi
  • Organizer: Random Matrican and Integrability Research Workshop of The Ismel Science Found〓
  • Place of Presentation: Yad Hashmona, Israel
  • Year and Date: 2009-03-26
• [Presentation] Intersection numbers from duality and replica (2009)
  • Author(s): S.Hikami
  • Organizer: ISF conference "Random matrices and replica"
  • Place of Presentation: Yad Hashmona, イスラエル
  • Year and Date: 2009-03-21
• [Presentation] Topological invariance in random matrices (2008)
  • Author(s): S.Hikami
  • Organizer: 99^<th> Statistical mechanics conference
  • Place of Presentation: ラトガース大学, 米国
  • Year and Date: 2008-05-11
• [Presentation] Topological Invariance in Random Matrices (2008)
  • Author(s): S. Hikami
  • Organizer: 99^<th> Statistical Mechanics Conference
  • Place of Presentation: Rutgers University
  • Year and Date: 2008-05-11
• [Remarks]
  • URL: http://dice.c.u-tokyo.ac.jp