Mathematics and Physics in Heidelberg Fakultät für Mathematik und Informatik Fakultät für Mathematik und Informatik Mathematisches Institut Karl-Theodor-Brücke Surprise Fakultät für Physik und Astronomie Fakultät für Physik und Astronomie Institut für Theoretische Physik Universität Heidelberg Universität Heidelberg Universität Heidelberg
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Lecture course in the Winter Semester 2017/18

Supergeometry and Supergravity


First lecture on October 16


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,

Time and Place:
Lectures on Monday & Wednesday, 9-11, MATHEMATIKON SR 5
Problems Sessions on Friday 11-1,MATHEMATIKON SR 9

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


Week Lecture topics Discussion topicsProblem 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


Coming soon...