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Direct approach to the mathematical structure of the equivalence between quantum field theories in different spacetime dimensions

Research Project

Project/Area Number 25870159
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Particle/Nuclear/Cosmic ray/Astro physics
Mathematical physics/Fundamental condensed matter physics
Research InstitutionThe University of Tokyo

Principal Investigator

Tachikawa Yuji  東京大学, カブリ数物連携宇宙研究機構, 教授 (10639587)

Project Period (FY) 2013-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywordsquantum field theory / mathematics / 場の量子論 / 超対称場の量子論 / 数理物理 / 超共形場理論 / 物性理論との関係 / 高次元の場の理論 / 超対称姓 / 超対称ゲージ理論 / 数学と理論物理の交流 / 超対称性ゲージ理論
Outline of Final Research Achievements

At the time of the grant application, only the equivalences of quantum field theories in different dimensions coming from 6d maximally supersymmetric theories were envisioned, following the original proposal made by me and coauthors Alday and Gaiotto. Since then, it became gradually clearer that one can obtain richer equivalences by starting from 6d minimally supersymmetric theories. For this reasons I put most of my efforts in studying the general properties of these 6d minimally supersymmetric theories. Among others, the formula for the quantum anomaly of general systems of this kind which I obtained with coauthors has been used widely in the literature. I also performed various related studies and gave multiple invited presentations.

Report

(6 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (31 results)

All 2018 2017 2016 2015 2014 2013 Other

All Journal Article (18 results) (of which Int'l Joint Research: 4 results,  Peer Reviewed: 18 results,  Open Access: 12 results,  Acknowledgement Compliant: 10 results) Presentation (11 results) (of which Int'l Joint Research: 5 results,  Invited: 11 results) Book (1 results) Remarks (1 results)

  • [Journal Article] On time-reversal anomaly of 2+1d topological phases2017

    • Author(s)
      Yuji Tachikawa, Kazuya Yonekura
    • Journal Title

      PTEP

      Volume: 2017 no.3 Issue: 3

    • DOI

      10.1093/ptep/ptx010

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Gauge interactions and topological phases of matter2016

    • Author(s)
      Yuji Tachikawa and Kazuya Yonekura
    • Journal Title

      PTEP

      Volume: 2016 no.9 Issue: 9 Pages: 093B07-093B07

    • DOI

      10.1093/ptep/ptw131

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Hofstadter's Butterfly in Quantum Geometry2016

    • Author(s)
      Yasuyuki Hatsuda, Hosho Katsura, and Yuji Tachikawa
    • Journal Title

      New. J. Phys.

      Volume: 18 Issue: 10 Pages: 1030231-16

    • DOI

      10.1088/1367-2630/18/10/103023

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Anomaly of strings in 6d N=(1,0) theories2016

    • Author(s)
      Hiroyuki Shimizu, Yuji Tachikawa and Gabi Zafrir
    • Journal Title

      Journal of High Energy Physics

      Volume: 165 Issue: 11 Pages: 1-12

    • DOI

      10.1007/jhep11(2016)165

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] 6d N=(1,0) theories on S1 /T2 and class S theories: part II2015

    • Author(s)
      K. Ohmori, H. Shimizu, Y. Tachikawa, K. Yonekura
    • Journal Title

      Journal of High Energy Physics

      Volume: 12 Issue: 12 Pages: 131-131

    • DOI

      10.1007/jhep12(2015)131

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] A review of the T_N theory and its cousins2015

    • Author(s)
      Y. Tachikawa
    • Journal Title

      Progress of Theoretical and Experimental Physics

      Volume: 2015 Issue: 11 Pages: 11B102-11B102

    • DOI

      10.1093/ptep/ptv098

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] On skein relations in class S theories2015

    • Author(s)
      Y. Tachikawa and N. Watanabe
    • Journal Title

      Journal of High Energy Physics

      Volume: 06 Issue: 6 Pages: 186-186

    • DOI

      10.1007/jhep06(2015)186

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Mass-deformed T_N as a linear quiver2015

    • Author(s)
      Hirotaka Hayashi, Yuji Tachikawa, Kazuya Yonekura
    • Journal Title

      Journal of High Energy Physics

      Volume: 02 Issue: 2 Pages: 089-089

    • DOI

      10.1007/jhep02(2015)089

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Magnetic discrete gauge field in the confining vacua and the supersymmetric index2015

    • Author(s)
      Yuji Tachikawa
    • Journal Title

      Journal of High Energy Physics

      Volume: 03 Issue: 3 Pages: 035-035

    • DOI

      10.1007/jhep03(2015)035

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Instanton operators and symmetry enhancement in 5d supersymmetric gauge theories2015

    • Author(s)
      Yuji Tachikawa
    • Journal Title

      Progress of Theoretical and Experimental Physics

      Volume: 043 Issue: 4

    • DOI

      10.1093/ptep/ptv040

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Anomaly polynomial of E-string theories2014

    • Author(s)
      Kantaro Ohmori, Hiroyuki Shimizu, Yuji Tachikawa
    • Journal Title

      Journal of High Energy Physics

      Volume: 08 Issue: 8 Pages: 002-015

    • DOI

      10.1007/jhep08(2014)002

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Anomaly polynomial of general 6d SCFTs2014

    • Author(s)
      Kantaro Ohmori, Hiroyuki Shimizu, Yuji Tachikawa, Kazuya Yonekura
    • Journal Title

      Progress of Theoretical and Experimental Physics

      Volume: B07 Issue: 10 Pages: 103-128

    • DOI

      10.1093/ptep/ptu140

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Elliptic genera of two-dimensional N=2 gauge theories with rank-one gauge groups2014

    • Author(s)
      Francesco Benini, Richard Eager, Kentaro Hori, Yuji Tachikawa
    • Journal Title

      Lett. Math. Phys

      Volume: 104 Issue: 4 Pages: 465-493

    • DOI

      10.1007/s11005-013-0673-y

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Reading between the lines of four-dimensional gauge theories2013

    • Author(s)
      O. Aharony, N. Seiberg, Y. Tachikawa
    • Journal Title

      Journal of High Energy Physics

      Volume: 1308 Issue: 8 Pages: 115-115

    • DOI

      10.1007/jhep08(2013)115

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] N=1 dynamics with TN theory2013

    • Author(s)
      K. Maruyoshi, Y. Tachikawa, W. Yan, K. Yonekura
    • Journal Title

      Journal of High Energy Physics

      Volume: 1310 Issue: 10 Pages: 10-10

    • DOI

      10.1007/jhep10(2013)010

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Dynamical Supersymmetry Breaking with TN Theory2013

    • Author(s)
      K. Maruyoshi, Y. Tachikawa, W. Yan, K. Yonekura
    • Journal Title

      Physics Review D

      Volume: 88 Issue: 8 Pages: 85037-85037

    • DOI

      10.1103/physrevd.88.085037

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] 2d SCFT from M2-branes2013

    • Author(s)
      Kentaro Hori, Chan. Y. Park, Yuji Tachikawa
    • Journal Title

      JHEP

      Volume: 1311 Issue: 11 Pages: 147-147

    • DOI

      10.1007/jhep11(2013)147

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Classification of 4d N=2 gauge theories2013

    • Author(s)
      L. Bhardwaj, Y. Tachikawa
    • Journal Title

      Journal of High Energy Physics

      Volume: 1312 Issue: 12 Pages: 100-100

    • DOI

      10.1007/jhep12(2013)100

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] Topological phases and relativistic quantum field theories2018

    • Author(s)
      Yuji Tachikawa
    • Organizer
      CERN Winter School on Supergravity, Strings and Gauge Theories
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On 4d N=3 theories2016

    • Author(s)
      Yuji Tachikawa
    • Organizer
      JHS75 (the 75th-year-anniversary conference for John H. Schwarz)
    • Place of Presentation
      California Institute for Technology, Pasadena, USA
    • Year and Date
      2016-11-18
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On the time-reversal anomaly of 2+1d TQFTs2016

    • Author(s)
      Yuji Tachikawa
    • Organizer
      Natifest (the 60th-year-anniversary conference for Nathan Seiberg)
    • Place of Presentation
      Institue for Advanced Study, Princeton, USA
    • Year and Date
      2016-09-15
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 6d SCFTs and F-theory: a bottom-up perspective2016

    • Author(s)
      Y. Tachikawa
    • Organizer
      F-theory @ 20 conference
    • Place of Presentation
      California Institute of Technology, Pasadena, California, United States of America
    • Year and Date
      2016-02-22
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On fractional M5 branes and frozen singularities2015

    • Author(s)
      Y. Tachikawa
    • Organizer
      KIAS-YITP workshop 2015
    • Place of Presentation
      Korea Institute for Advanced Studies, Seoul, South Korea
    • Year and Date
      2015-09-15
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Twenty Years of the Seiberg-Witten Theory2014

    • Author(s)
      Yuji Tachikawa
    • Organizer
      String Theory and Mathematical Sciences in the 21st Century
    • Place of Presentation
      京都、国立京都国際会館
    • Year and Date
      2014-11-12
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Comments on SUSY Quantum Field Theories2014

    • Author(s)
      Yuji Tachikawa
    • Organizer
      XXXth International Colloquium on Group Theoretical Methods in Physics
    • Place of Presentation
      Ghent, Belgium
    • Year and Date
      2014-07-14 – 2014-07-18
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Recent Advances in SUSY2014

    • Author(s)
      Yuji Tachikawa
    • Organizer
      Strings 2014
    • Place of Presentation
      Princeton, New Jersey, USA
    • Year and Date
      2014-06-23 – 2014-06-27
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] On lines in class-S theories and in q-deformed Yang-Mills2014

    • Author(s)
      Y. Tachikawa
    • Organizer
      Integrability, Symmetry and Quantum Space-Time, 2014
    • Place of Presentation
      京都大学基礎物理研究所(京都府)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Line operators and dualities of 4d gauge theories2013

    • Author(s)
      Y. Tachikawa
    • Organizer
      Workshop on Gauge and String Theory
    • Place of Presentation
      東京大学高等研究所 Kavli 数物連携宇宙研究機構 (千葉県)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] On some conjectures extracted from supersymmetric quantum field theories2013

    • Author(s)
      立川裕二
    • Organizer
      第 16 回 代数群と量子群の表現論
    • Place of Presentation
      箱根強羅静雲荘(神奈川県)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Book] N=2 Supersymmetric Dynamics for Pedestrians2015

    • Author(s)
      Yuji Tachikawa
    • Total Pages
      224
    • Publisher
      Springer
    • Related Report
      2014 Research-status Report
  • [Remarks] Topological Phases and Relativistic QFTs

    • URL

      https://member.ipmu.jp/yuji.tachikawa/lectures/2018-cern-rikkyo/

    • Related Report
      2017 Annual Research Report

URL: 

Published: 2014-07-25   Modified: 2019-07-29  

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