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

2017 Fiscal Year Final Research Report

• 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
• Keywords: quantum field theory / mathematics

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.

Free Research Field

string theory, mathematical physics