Electric-Magnetic Duality and Physics of Geometric Langlands

Learning Seminar, Fall 2020

Overview:

This is a learning seminar about EM duality and the physics of Geometric Langlands. The current plan is to understand S duality in 4D N=4 Yang Mills. From there, we follow Kapustin-Witten to see how S-duality connects to geometric Langlands.

Schedule:

Date Topic Speaker
9/21 Organization meeting/intro
9/28 N=2 SUSY Yang-Mills Leon Liu
10/5 N= SUSY Yang-Mills Leon Liu
10/12 SUSY algebra and topological twistings Grant Elliot
10/19 Topological twistings part II Grant Elliot
10/26 Kahler geometry and Hitchin's moduli space Sebastian Schulz
11/9 Introduction to Geometric Langlands Leon Liu
11/16 Abelian duality in TFT Leon Liu

References:

[1]
A. Kapustin and E. Witten. Electric-Magnetic Duality and the Geometric Langlands Program. Comm. in N.T. and Physics (2006) Vol. 1

[2]
O'Farrill. Electromagnetic Duality for Children. Good lecture notes on electric-magnetic duality in N=4 4D gauge theories.

[3]
E. Witten. Mirror Manifolds and Topological Field Theory.

Useful links:

[1]
D. Tong. Lectures on gauge theory. Great introduction to gauge theories.

[2]
C. Elliott. An algebraic introduction to Kapustin-Witten theory.

[3]
A. Balasubramanian. A survey of Literature on gauge theory approach to Geometric Langlands.

[4]
E. Frenkel. Lectures on the Langlands Programm and Conformal Field Theory . Good intro to Langlands program.
[5]
L. Gaume and S. Hassan. Introduction to S-duality in N=2 SUSY gauge theories

[6]
N. Seiberg, E. Witten. Monopole condensation and confinement in N=2 SUSY YMs. Nuc. Phys. B 431, no. 3.