Understanding Fermionic Generalized Symmetries

Abstract

We explore new aspects of internal fermionic shifting symmetries, present in physical systems such as free Dirac spinors and p-form tensor-spinor fields. We propose a novel procedure to gauge these global symmetries, which also introduces a new Stückelberg mechanism to give a mass to free fermionic fields. Furthermore, we find new magnetic fermionic symmetries in these physical systems whose charged objects are disorder operators. For the case of a Dirac spinor, we discuss an dual description, where the magnetic symmetry acts on the holonomies of a dual 2-form tensor-spinor. Further generalizations such as higher-group-like structures are also discussed.

5 pages plus 3 appendices. v3: Added Appendix C: "Hamiltonian analysis of coupled systems", typos fixed, references added