Aspects of Supersymmetry

Welcome to the wikipage for the course Aspects of Supersymmetry.

The plan of the course is to be an unorthodox introduction to several aspects of supersymmetric field theories.

The program is going to be built as we go along -- among the aims is to give you a sketch of several basic tricks of the trade as well as to expose you to materials that are useful in the context of higher dimensional superconformal systems and their compactifications.

We will meet weekly on Fridays from 16 to 17 during term time.

Sometimes, the seminar might be replaced by a quiver meeting seminar which we can stream together.

If you are a PhD student and want to add this course to your studyplan, we can discuss about this with your supervisor. If you are a master student since this course is a reading course, if you want this course to be recognized it should be part of a small `research project'.

Lecture 1: Introduction - Supersymmetry in 2022
March 18. Room 4003.

High-energy physicists were all very excited about supersymmetry, till they looked for it using LHC and they have not found it (so far).

So why should we bother studying supersymmetry if it does not work?

In this lecture we will pose and answer the above question and motivate the study of supersymmetric field theory independently of their applications to particle physics phenomenology.

We have also talked about the Coleman-Mandula theorem.

References: W, III,Pr.; W, III,Ch. 24; B. Richer, Is naturalness unnatural?; M. Strassler, New Signals and Challenges for LHC

Lecture 2: General Structure of Poincaré Supersymmetry in Various Dimensions
March 25. Room 4004.

In this lecture and the next we will derive the structures of Poincaré Supersymmetry in various dimensions. The relation with division algebras will be emphasized.

The main result of this lecture is to determine the general structure of Poincaré supersymmetry algebras in Minkowski spacetimes with signature (D-1,1). We will see that supercharges must all have half-integer spins, and hence transform as fundamental spinors, that they have to commute with all momenta, and from this deduce that Poincaré supersymmetry algebras have a very specific form. We will conclude deriving the properties of the central charges.

References: W, III, Ch. 32

Lecture 3,4: Detailed Structure of Poincaré Supersymmetry in Various Dimensions
April 8. Room 4003. April 29. Room 4003.

In these lectures, we will dive into the structure of supersymmetry algebras building on the properties of D dimensional spinors. We will see the pattern R, C, H, and " O " emerge along the way.

In the first of the lectures devoted to the detailed structure of spinors we have explained the logic of our analysis: our approach to this problem is to exploit the structure of Clifford algebras to build the corresponding fundamental spinors as modules. In the second lecture we will establish Bott periodicity and explain the Clifford checkerboard.

References: W, III, Ch. 32; C,Ch 2; P. Deligne, Notes on Spinors; For an example of 3d SUSY algebra with non central charges see appendix E of Maldacena, Lin, arXiv:hep-th/0509235

Desiderata
Please add here papers that we want to study during one of these sessions. Use the following format:


 * Edward Witten, Supersymmetric Index In Four-Dimensional Gauge Theories (2000)

Participants
Athanasios Voutouras

Azeem Hasan

Charles Thull

Chen Huang

Daniel Panizo Pérez

Elias Riedel Gårding

Evangelos Tsolakidis

Filippo Balli

Giulia Fardelli

Matthew Magill

Muyang Liu

Lorenzo Ruggeri

Paul-Konstantin Oehlmann

Robert Moscrop

Roman Mauch

Shani Nadir Meynet

Simon Douaud

Simon Ekhammar

Vladimir Bashmakov

Zhou Zheng