News
First lecture on October 16Description
Ideas of supersymmetry play a central role in formal theoretical high-energy physics and in relating quantum theory to geometry. In AdS/CFT, classical supergravity is the starting point for understanding strongly coupled quantum field theory. The aim of this course is to discover the mathematical foundations of supersymmetry and to learn the geometric language underlying classical supergravity.
Prerequisites: Solid knowledge of differential geometry, basics of Lie theory and symmetric spaces, some quantum field theory and general relativity.
Instructor: Prof. J. Walcher, walcher@uni-heidelberg.de
Time and Place:
Lectures on Monday & Wednesday, 9-11, MATHEMATIKON SR 5
Problems Sessions on Friday 11-1,MATHEMATIKON SR 9
References:
Freedman and van Proeyen, Supergravity
Cecotti, Supersymmetric field theory. Geometric structures and dualities
Deligne and Freed, Quantum fields and strings (IAS Lectures)
Castellani, D'Auria, and Fré, Supergravity and superstrings. A geometric perspective
Plan
| Week | Lecture topics | Discussion topics | Problem set |
|---|---|---|---|
| October 16 | Introduction and overview | super linear algebra | |
| October 23 | Clifford algebras and modules | tensor categories | Homework 1 |
| October 30 | Spinors | \(G_2\) and triangulations of \(\mathbb R\mathbb P^2\) | Homework 2 |
| November 6 | Supersymmetry in relativistic QM | ||
| November 13 | Supermultiplets | The functor of points | Homework 3 |
| November 20 | Super Lie groups | ||
| November 27 | Supermanifolds I | The superparticle | |
| December 4 | Supermanifolds II | \({\it GL}(n|m)\), \({\it SL}(n|m)\), and \({\it OSp}(n|m)\) | |
| December 11 | Superintegration | Superconformal symmetry | |
| December 18 | Superfields | ||
| January 8 | Cartan geometry I | Super-Moduli | |
| January 15 | Cartan geometry II | AKSZ I | |
| January 22 | Variational principles I | AKSZ II | Homework 4 |
| January 29 | Variational principles II | AKSZ III |
Evaluation
Coming soon...