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ブレーンタイリングによる箙ゲージ理論の研究及びその応用

Research Project

Project/Area Number 08J08802
Research Category

Grant-in-Aid for JSPS Fellows

Allocation TypeSingle-year Grants
Section国内
Research Field Particle/Nuclear/Cosmic ray/Astro physics
Research InstitutionThe University of Tokyo

Principal Investigator

山崎 雅人  東京大学, 数物連携宇宙研究機構, 特別研究員(PD)

Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 2010: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2009: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2008: ¥600,000 (Direct Cost: ¥600,000)
Keywords素粒子理論 / 超弦理論 / BPS状態の数え上げ / 壁超え現象 / 行列模型 / 箙ゲージ理論 / 位相的弦理論 / ゲージ理論 / Dブレーン / ブレーンタイリング / F理論 / M理論 / 結晶溶解
Research Abstract

20世紀物理学の最大の成果は一般相対性理論と量子力学であるが、この二つは両立しないことが知られている。超弦理論は、この二つを矛盾なく統合する量子重力の理論の最有力候補である。この超弦理論において本質的な役割を果たすのがDブレーンと呼ばれるものであり、本研究はDブレーンを扱う方法(その例として本研究の表題にあるブレーンタイリングがあげられる)を駆使し、超対称ゲージ理論や超弦理論の理解を深め、量子的な幾何学とは何かを理解しようとするものである。
研究の最終年度にあたる本年は、これまで著者らが提唱してきた結晶の溶解模型を使って、BPS状態の数え上げにおける壁超え現象をさらに精密に理解することを目標とした。より具体的には、筆者はカリフォルニア工科大学の大栗、Sulkowskiの両氏と共同でBPS状態の数え上げに現れる分配関数を行列模型の立場から再解釈した(Communications in Mathematical Physicsに受理済)。これはBPS状態の数え上げの問題に行列模型のテクニックを応用することを可能にするものであり、一例として我々は行列模型のスペクトラル曲線上の位相的弦理論がBPS状態の数え上げを再現することを示した。筆者はさらに統計力学系との対応を調べ、6月に京都に開催された会議のプロシーディングとしてまとめた。
本研究は筆者がプリンストン高等研究所に移動するに伴い中断となったが、関連した研究を現在も継続しており、またいくつかのフォローアップ論文もプレプリントサーバーにあがっており、さらなる発展が期待される。

Report

(3 results)
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (29 results)

All 2011 2010 2009 2008 Other

All Journal Article (17 results) (of which Peer Reviewed: 17 results) Presentation (11 results) Remarks (1 results)

  • [Journal Article] Crystal Melting and Wall Crossing Phenomena2011

    • Author(s)
      Masahito Yamazaki
    • Journal Title

      International Journal of Modern Physics A

      Volume: 26 Pages: 1097-1338

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A note on dimer models and McKay Quivers2010

    • Author(s)
      Kazushi Ueda, Masahito Yamazaki
    • Journal Title

      Communications in Mathematical Physics

      Volume: 301 Pages: 723-747

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Aspects of non-minimal gauge mediation2010

    • Author(s)
      Satoshi Shirai, Masahito Yamazaki, Kazuya Yonekura
    • Journal Title

      Journal of High Energy Physics

      Volume: 06 Pages: 56-56

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Open BPS Wall Crossing and M-theory2010

    • Author(s)
      Mina Aganagic, Masahito Yamazaki
    • Journal Title

      Nuclear Physics B

      Volume: 834 Pages: 258-272

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Crystal Melting and Toric Calabi-Yau Manifolds2009

    • Author(s)
      Hirosi Ooguri, Masahito Yamazaki
    • Journal Title

      Communications in Mathematical Physics 292

      Pages: 179-199

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Emergent Calabi-Yau Geometry2009

    • Author(s)
      Hirosi Ooguri, Masahito Yamazaki
    • Journal Title

      Physical Review Letters 102

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Coset Construction for Duals of Non-relativistic CFTs2009

    • Author(s)
      Sakura Schafer-Nameki, Kentaroh Yashida, Masahito Yamazaki
    • Journal Title

      Journal of High Energy Physics 905

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Emergent Calabi-Yau Geometry2009

    • Author(s)
      Hirosi Ooguri, Masahito Yamazaki
    • Journal Title

      Physical Review Letters ((印刷中)掲載確定)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Crystal Melting and Toric Calabi-Yau Manifolds2009

    • Author(s)
      Hirosi Ooguri, Masahito Yamazaki
    • Journal Title

      Communications in mathematical Physics ((印刷中)掲載確定)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Brane Tilings and Their Applications2008

    • Author(s)
      Masahito Yamazaki
    • Journal Title

      Fortschritte der Physik 56

      Pages: 555-686

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] New Aspects of Heterotic--F Theory Duality2008

    • Author(s)
      Hirotaka Hayashi, et. al.
    • Journal Title

      Nuclear Physics B 806

      Pages: 224-299

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Intersecting Solitons, Amoeba and Tropical Geometry2008

    • Author(s)
      Toshiaki Fujimori, et. al.
    • Journal Title

      Physical Review D 78

      Pages: 1005004-1005004

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A New N=4 Membrane Action via Orbirold2008

    • Author(s)
      Hiroyuki Fuji, Seiji Terashima, Masahito Yamazaki
    • Journal Title

      Nuclear Physics B 810

      Pages: 354-368

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Octonions, G2 and Generalized Lie 3-algebras2008

    • Author(s)
      Masahito Yamazaki
    • Journal Title

      Physics Letters B 670

      Pages: 215-219

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Toric Calabi-Yau four-folds dual to Chern-Simons-matter theories2008

    • Author(s)
      Kazushi Ueda, Masahito Yamazaki
    • Journal Title

      Journal of High Energy Physics 12

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Moduli Stabilization in Stringy ISS Models2008

    • Author(s)
      Masahito Yamazaki
    • Journal Title

      International Journal of Modern Physics A 23

      Pages: 2190-2191

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Comments on orientifold of brane tilings2008

    • Author(s)
      Yosuke Imamura, Keisuke Kimura, Masahito Yamazaki
    • Journal Title

      International Journal of Modern Physics A 23

      Pages: 2299-2306

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] Dimer, crystal, free fermion and wall-crossing2010

    • Author(s)
      Masahito Yamazaki
    • Organizer
      Developments in Quantum Integrable Systems
    • Place of Presentation
      京大数理解析研究所
    • Year and Date
      2010-06-16
    • Related Report
      2010 Annual Research Report
  • [Presentation] Amoeba, coamoeba and non-commutative Donaldson-Thomas Invariants2010

    • Author(s)
      山崎雅人
    • Organizer
      Conference on Tropical Geometry and Mirror Symmetry
    • Place of Presentation
      UC San Diego USA
    • Year and Date
      2010-02-14
    • Related Report
      2009 Annual Research Report
  • [Presentation] 一般化されたLie 3-代数の構成と八元数2009

    • Author(s)
      山崎雅人
    • Organizer
      日本物理学会
    • Place of Presentation
      甲南大学
    • Year and Date
      2009-09-13
    • Related Report
      2009 Annual Research Report
  • [Presentation] Coset 構成による非相対論的共形場理論の重力双対の構成2009

    • Author(s)
      山崎雅人
    • Organizer
      日本物理学会
    • Place of Presentation
      甲南大学
    • Year and Date
      2009-09-11
    • Related Report
      2009 Annual Research Report
  • [Presentation] 結晶溶解とBPS状態の数え上げ2009

    • Author(s)
      山崎雅人
    • Organizer
      日本物理学会
    • Place of Presentation
      甲南大学
    • Year and Date
      2009-09-11
    • Related Report
      2009 Annual Research Report
  • [Presentation] Wall Crossing and M-theory2009

    • Author(s)
      山崎雅人
    • Organizer
      Simons Workshop in Mathematics and Physics 2010
    • Place of Presentation
      Stony Brook, USA
    • Year and Date
      2009-08-11
    • Related Report
      2009 Annual Research Report
  • [Presentation] Crystal Melting and Wall Crossing Phenomena2009

    • Author(s)
      山崎雅人
    • Organizer
      Focus Week on New Invariants and Wall Crossings
    • Place of Presentation
      東京大学IPMU
    • Year and Date
      2009-05-21
    • Related Report
      2009 Annual Research Report
  • [Presentation] Crystal Melting and Non-commutative Donaldson-Thomas Theory2009

    • Author(s)
      Masahito Yamazaki
    • Organizer
      Dualities in Physics and Mathematics
    • Place of Presentation
      KITP
    • Year and Date
      2009-03-20
    • Related Report
      2008 Annual Research Report
  • [Presentation] A New N=4 Membrane Action via Orbifold2008

    • Author(s)
      寺嶋靖治, 藤博之, 山崎雅人
    • Organizer
      日本物理学会秋季大会
    • Place of Presentation
      山形大学
    • Year and Date
      2008-09-22
    • Related Report
      2008 Annual Research Report
  • [Presentation] A New N=4 Membrane Action via Orbifold2008

    • Author(s)
      寺嶋靖治, 藤博之, 山崎雅人
    • Organizer
      基礎物理学研究所研究会「量子場の理論と弦理論の発展」
    • Place of Presentation
      京都大学基礎物理学研究所
    • Year and Date
      2008-07-30
    • Related Report
      2008 Annual Research Report
  • [Presentation] Quiver Chern-Simons-matter 理論とAdS4/CFT3対応2008

    • Author(s)
      植田一石, 山崎雅人
    • Organizer
      日本物理学会第64回年次大会
    • Place of Presentation
      立教大学
    • Year and Date
      2008-03-29
    • Related Report
      2008 Annual Research Report
  • [Remarks]

    • URL

      http://www.princeton.edu/~masahito/

    • Related Report
      2010 Annual Research Report

URL: 

Published: 2008-04-01   Modified: 2024-03-26  

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