2016/08/31 by Yuji Tachikawa
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Function (biology) #Gauge theory #Mathematical physics #Mathematics #Particle physics theoretical and experimental studies #Partition function (quantum field theory) #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Theoretical physics #Yang–Mills theory #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/1751-8121/aa5df8
This is a contribution to the review volume `Localization techniques in quantum field theories' (eds. V. Pestun and M. Zabzine) which contains 17 Chapters. The complete volume is summarized in arXiv:1608.02952 and it can be downloaded at https://arxiv.org/src/1608.02952/anc/LocQFT.pdf or http://pestun.ihes.fr/pages/LocalizationReview/LocQFT.pdf v4: a reference corrected
arxiv created 2016/10/15 · openalex publication_date 2017/10/13 · arxiv updated 2017/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Abstract An elementary introduction to the 2d/4d correspondences is given. After quickly reviewing the 2d q -deformed Yang–Mills theory and the Liouville theory, we will introduce 4d theories obtained by coupling trifundamentals to SU(2) gauge fields. We will then cleraly see that the supersymmetric partition function of these theories on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:msup> <mml:mi>S</mml:mi> <mml:mn>3</mml:mn> </mml:msup> <mml:mo>×</mml:mo> <mml:msup> <mml:mi>S</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:mstyle> </mml:math> and on S 4 is given, respectively, by the q -deformed Yang–Mills theory and the Liouville theory. After giving a short discussion on how this correspondence may be understood from the viewpoint of the 6d <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mrow> <mml:mi mathvariant="script">N</mml:mi> </mml:mrow> <mml:mo>=</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>0</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mstyle> </mml:math> theory, we conclude the review by enumerating future directions. Most of the technical points will be referred to more detailed review articles.