Generalized Global Symmetries

Generalized Global Symmetries are a relatively recent addendum to the quantum field theory dictionary that is playing a pivotal role in recent developments in the subject.

We will begin our discussion about generalized global symmetries with an in depth review of the paper [1].

2020-02-26: The definition of a global symmetry in QFT (Michele)

 * Motivations for generalized global symmetries [1], Section 1.


 * Revised definition of ordinary symmetry in quantum field theory [1], Section 2. AIM: give a definition that does not depend on a Lagrangian formulation.


 * Examples: ordinary U(1) and Z/nZ


 * The definition easily generalizes: definition of higher form symmetry [1], Section 3.

2020-03-11: More about the definition of generalized global symmetries (Michele)

 * Comments about selection rules


 * Examples of generalized global symmetries

2020-04-01: More examples of generalized global symmetries (Usman)
Usman will discuss the content of Sections 4.2, 4.3 and 4.4 of [1].

2020-04-15: 't Hooft anomalies for higher form symmetries (Luca)
Luca will discuss the content of Section 4.4 of [1]. Lecture notes

2020-04-21: IIB flux non-commutativity and the global structure of field theories (Iñaki García-Extebarria - Nordic Seminar)
I will discuss the origin of the choice of global structure (or equivalently, the choice for which higher p-form symmetries are present in the theory) for various Lagrangian and non-Lagrangian field theories in terms of their realization in IIB and M-theory. I will explain how this choice on the field theory side can be traced back to the fact that fluxes in string/M-theory do not commute in the presence of torsion. I will illustrate how these ideas provide a stringy explanation for the fact that six-dimensional (2,0) and (1,0) theories generically have a partition vector (as opposed to a partition function) and explain how this reproduces the classification of N=4 theories provided by Aharony, Seiberg and Tachikawa. Time permitting, I will describe how to use these ideas to determine the global structure for the Argyres-Douglas theories, and how this can be used to test recently proposed N=1 Lagrangians for some of these theories.

The slides of the talk are available following this link

2020-04-29: 't Hooft anomalies for higher form symmetries (Luca)
Luca will continue to discuss 't Hooft anomalies. Lecture notes

2020-06-04: Higher Form Symmetries and M-theory (Michele)
Discussion about the realization of higher form symmetries in M-theory.
 * Defect group
 * Geometric engineering Hilbert space
 * Non-commutative fluxes

Applications to the study of higher form symmetries of 5d SCFTs.