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Advanced aspects of symmetries

Informations pratiques

Discipline :


Niveau :

master 2

Semestre :


Crédits ECTS :


Volume Horaire :

24h Cours
12h TD

Responsable :


Université de Savoie, Laboratoire d’Annecy-le-Vieux de Physique Théorique

Intervenants :

François DELDUC



This course provides a basic introduction to conformal symmetry and supersymmetry, both of which play an important role in modern physical theories. Conformal transformations in arbitrary dimensions are characterised by leaving the space-time metric invariant up to a (local) scaling factor. They appear in a vast spectrum of physical applications, ranging from condensed matter to string theory and modern particle physics. Supersymmetry relates bosonic and fermionic fields to each other. While not yet directly observed at the energies of current collider experiments like the LHC, supersymmetry plays an important role in extending the standard model and in approaching important fundamental questions of modern high energy physics. This course starts with a mathematical description of both symmetries using a group theoretic language and explores their applications to field theories in various dimensions.


Plan du cours


Part 1:  Conformal Symmetry
- the conformal group in arbitrary dimensions

- correlation functions in conformal field theories
- two-dimensional conformal theories and the Virasoro algebra

Part 2:  Supersymmetry
- Coleman-Mandula theorem and superalgebras

- superspaces
- representation theory: supermultiplets

- supersymmetric field theories


Langue d'enseignement


This set of lectures will be given in English.



Basic knowledge of geometry, group theory and quantum field theories



- P. Di Francesco, P. Mathieu and D. Senechal, "Conformal Field Theory" 

- J. Wess, J. Bagger, "Supersymmetry and Supergravity"

Modalité de l'examen

Written exam