course dates credits
Generalized symmetries: Theory and Practice May 9 - Jun 9 -
teachers schedule term
Christian Copetti Tue, Fri, 14:00 - 16:00 adv


Various generalizations of the concept of symmetry have been introduced in the last ten years, allowing to refine many questions about the dynamics of interacting QFTs.

The aim of the course is to introduce such new developments in a pedagogical way, so that the audience should be able to approach the modern literature with confidence.

The program will be (roughly) as follows:

  • PART I Higher form symmetries
    • Some concepts from (co)homology theory
    • Discrete symmetries, defects and gauge fields
    • Higher form symmetries
    • Gapped realizations (SPTs and TQFTs)
    • Gauging and anomalies
    • Mixed anomalies and Higher Groups
  • PART II ``Categorical'' symmetries in d=2
    • What is a categorical symmetry: Fusion categories
    • Gauging and anomalies: Frobenius algebras
    • (Time permitting) action on local operators: the Tube algebra
    • RCFT realizations and examples: self dualities and Tambara Yamagami categories
    • Gapped realizations and SSB
  • PART III ``Categorical'' symmetries in d=4
    • What is a categorical symmetry (take II) ?
    • Higher gauging and condensation defects
    • Self duality defects (take II): N=4 SYM
    • Gapped RG flows and SSB: N=1*
    • ABJ anomalies and KOZ symmetries
    • Current developments and open questions


The course will to be self contained, however some background reading could prove useful:

  • It would be useful to know what are 't Hooft anomalies for usual continuous symmetries, such as U(1)^3 chiral anomalies and what is ``anomaly inflow''. A good reference might be arXiv: 0802.0634.
  • For Part II it would be useful to rehearse 2d CFTs, especially the Ising CFT and the c=1 theories (the lectures of Ginsparg are an excellent reference arXiv:hep-th/9108028 )
  • For Part III some preliminary knowledge about N=4 SYM and Montonen Olive duality could be useful.


Online Resources:

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