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

• Project/Area Number: 25870159
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Particle/Nuclear/Cosmic ray/Astro physics; Mathematical physics/Fundamental condensed matter physics
• Research Institution: The 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: ¥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)
• Keywords: quantum 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.

Research Products

• [Journal Article] On time-reversal anomaly of 2+1d topological phases (2017)
  • Author(s): Yuji Tachikawa, Kazuya Yonekura
  • Journal Title: PTEP Volume: 2017 no.3 Issue: 3
  • DOI: 10.1093/ptep/ptx010
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Gauge interactions and topological phases of matter (2016)
  • Author(s): Yuji Tachikawa and Kazuya Yonekura
  • Journal Title: PTEP Volume: 2016 no.9 Issue: 9 Pages: 093B07-093B07
  • DOI: 10.1093/ptep/ptw131
  • Peer Reviewed / Open Access
• [Journal Article] Hofstadter's Butterfly in Quantum Geometry (2016)
  • 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
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Anomaly of strings in 6d N=(1,0) theories (2016)
  • 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
  • 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 II (2015)
  • 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
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] A review of the T_N theory and its cousins (2015)
  • Author(s): Y. Tachikawa
  • Journal Title: Progress of Theoretical and Experimental Physics Volume: 2015 Issue: 11 Pages: 11B102-11B102
  • DOI: 10.1093/ptep/ptv098
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] On skein relations in class S theories (2015)
  • 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
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Mass-deformed T_N as a linear quiver (2015)
  • 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
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Magnetic discrete gauge field in the confining vacua and the supersymmetric index (2015)
  • Author(s): Yuji Tachikawa
  • Journal Title: Journal of High Energy Physics Volume: 03 Issue: 3 Pages: 035-035
  • DOI: 10.1007/jhep03(2015)035
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Instanton operators and symmetry enhancement in 5d supersymmetric gauge theories (2015)
  • Author(s): Yuji Tachikawa
  • Journal Title: Progress of Theoretical and Experimental Physics Volume: 043 Issue: 4
  • DOI: 10.1093/ptep/ptv040
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Anomaly polynomial of E-string theories (2014)
  • 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
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Anomaly polynomial of general 6d SCFTs (2014)
  • 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
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Elliptic genera of two-dimensional N=2 gauge theories with rank-one gauge groups (2014)
  • 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
  • Peer Reviewed
• [Journal Article] Reading between the lines of four-dimensional gauge theories (2013)
  • 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
  • Peer Reviewed
• [Journal Article] N=1 dynamics with TN theory (2013)
  • 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
  • Peer Reviewed
• [Journal Article] Dynamical Supersymmetry Breaking with TN Theory (2013)
  • 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
  • Peer Reviewed
• [Journal Article] 2d SCFT from M2-branes (2013)
  • 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
  • Peer Reviewed
• [Journal Article] Classification of 4d N=2 gauge theories (2013)
  • 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
  • Peer Reviewed
• [Presentation] Topological phases and relativistic quantum field theories (2018)
  • Author(s): Yuji Tachikawa
  • Organizer: CERN Winter School on Supergravity, Strings and Gauge Theories
  • Int'l Joint Research / Invited
• [Presentation] On 4d N=3 theories (2016)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] On the time-reversal anomaly of 2+1d TQFTs (2016)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] 6d SCFTs and F-theory: a bottom-up perspective (2016)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] On fractional M5 branes and frozen singularities (2015)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] Twenty Years of the Seiberg-Witten Theory (2014)
  • 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
  • Invited
• [Presentation] Comments on SUSY Quantum Field Theories (2014)
  • 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
  • Invited
• [Presentation] Recent Advances in SUSY (2014)
  • Author(s): Yuji Tachikawa
  • Organizer: Strings 2014
  • Place of Presentation: Princeton, New Jersey, USA
  • Year and Date: 2014-06-23 – 2014-06-27
  • Invited
• [Presentation] On lines in class-S theories and in q-deformed Yang-Mills (2014)
  • 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)
  • Invited
• [Presentation] Line operators and dualities of 4d gauge theories (2013)
  • 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)
  • Invited
• [Presentation] On some conjectures extracted from supersymmetric quantum field theories (2013)
  • 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)
  • Invited
• [Book] N=2 Supersymmetric Dynamics for Pedestrians (2015)
  • Author(s): Yuji Tachikawa
  • Total Pages: 224
  • Publisher: Springer
• [Remarks] Topological Phases and Relativistic QFTs
  • URL: https://member.ipmu.jp/yuji.tachikawa/lectures/2018-cern-rikkyo/