Supersymmetric Gauge Theories - 1

(w/ Abhishek Chowdhury and Timm Wrase @ TU Vienna)

Organizational information

Every Wednesdays, starting 04-October-2017, at 16:00 Hrs at the SEM-138A Freihaus 7th Floor.
Please contact Abhiram in case of further information or clarifications.

Topics

  1. N = 2, d = 4 supersymmetric gauge theories
  2. Seiberg-Witten theory and exact solutions
  3. Four manifold invariants
  4. Dualities in various dimensions
  5. 6d N = (2,0) superconformal field theories

Pre-requisites

A good grasp of quantum field theory, differential geometry and supersymmetry is required for this course. Knowledge of conformal field theory is beneficial.

List of talks/lectures

04.10.2017: Organizational meeting + Introduction to supersymmetry - Abhiram Kidambi

11.10.2017: Non-perturbative aspects of QFT - Florian Hechenberger

18.10.2017: N=2 actions - Christoph Roupec

25.10.2017: N=2 actions + Twisted N=2 theory - Abhiram Kidambi

01.11.2017: All Souls Day, holiday

08.11.2017: Exact solutions to N=2 SU(2) gauge theory - Timm Wrase

15.11.2017: Nekrasov PF and Instanton Counting - Andreas Banlaki (St. Leopold day, still a working day. Change of time and location: Start at 15:00 sharp, Freihaus, Seminarraum 03 Stock, Gelb)

22.11.2017: 4-manifold invariants - Frederic Brunner

29.11.2017: 4-manifold invariants - Frederic Brunner

06.12.2017: Dualities in supersymmetric field theories - Abhishek Chowdhury

13.12.2017: Argyres-Douglas theory - Abhishek Chowdhury

20.12.2017: AGT correspondence and 2d/4d duality - Abhishek Chowdhury

10.01.2018: 6d (2,0) SCFT -I - Marcus Sperling

17.01.2018: 6d (2,0) SCFT -II - Johanna Knapp

12.02.2018: Seiberg like dualities and their string origin I- Abhiram Kidambi

14.02.2018: Seiberg like dualities and their string origin II - Abhiram Kidambi (Canceled)

Literature

The main literature for this course will be the book by Yuji Tachikawa titled N=2 dynamics for pedestrians. We will use this book as a skeleton and, as and when required, go over a few topics in more detail. The topics on wall crossing and geometric Langlands are not discussed in the book by Tachikawa and therefore, we have listed a few resources below. The extra references are to be used to supplement the book and are meant to be a further resource which one can consult for clarifications.

Extra references

For beginning (N=2) gauge theory and non-perturbative physics
  • N=2 dynamics for pedestrians(This book will form most of the pedagogical part of the course, both content and structure wise.)
  • John Preskill's 'Field Theory and Topology' course @ Caltech (Fantastic lectures!)
  • Electromagnetic duality for children
    • Seiberg-Witten theory
  • Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
  • Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
  • The Power of Holomorphy - Exact Results in 4D SUSY Field Theories
  • Seiberg-Witten Prepotential From Instanton Counting
  • Introduction to Seiberg-Witten Theory and its Stringy Origin
  • Introduction to S-Duality in N=2 Supersymmetric Gauge Theory. (A pedagogical review of the work of Seiberg and Witten)
    • Four manifold invariants
  • The Geometry of Four-manifolds
  • Monopoles and Four-Manifolds
  • Lectures On The Physical Approach To Donaldson And Seiberg-Witten Invariants Of Four-Manifolds by Greg Moore
    • \(\mathcal{N} = 1\) Dualities
  • Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories
  • IR Duality in d=3 N=2 Supersymmetric USp(2N_c) and U(N_c) Gauge Theories
  • 3d dualities from 4d dualities
  • Lectures on supersymmetric gauge theories and electric-magnetic duality
  • Brane dynamics and gauge theory
  • Type IIB Superstrings, BPS Monopoles, And Three-Dimensional Gauge Dynamics
    • 6d (2,0) SCFT
  • Flex Klein lectures by Greg Moore

    • Text books

    1. Geometry, Topology and Physics by Nakahara
    2. Aspects of Symmetry by Sidney Coleman
    3. Gauge Theory and Variational Principles by David Bleecker
    4. Supersymmetry and Supergravity by Wess and Bagger

    Video lectures

    1. PiTP Princeton 2010 (almost all of the topics we will go over in this course are covered fantastically by the experts and developers of said theories.)

    Lighter reading (but still quite technical)

    1. The Dawning of Gauge Theory by Lochlainn O'Raifeartaigh