We discuss aspects of global and gauged symmetries in quantum field theory and quantum gravity, focusing on discrete gauge symmetries. An effective Lagrangian description of ${\mathbb{Z}}_p$ gauge theories shows that they are associated with an emergent ${\mathbb{Z}}_p$ 1-form (Kalb-Ramond) gauge symmetry. This understanding leads us to uncover new observables and new phenomena in nonlinear $\sigma$ models. It also allows us to expand on Polchinski’s classification of cosmic strings. We argue that in models of quantum gravity, there are no global symmetries, all continuous gauge symmetries are compact, and all charges allowed by Dirac quantization are present in the spectrum. These conjectures are not new, but we present them from a streamlined and unified perspective. Finally, our discussion about string charges and symmetries leads to a more physical and more complete understanding of recently found consistency conditions of supergravity.

• Received 25 January 2011

DOI:https://doi.org/10.1103/PhysRevD.83.084019

This article appears in the following collection:

Physical Review D 50^th Anniversary Milestones

This collection of seminal papers from PRD highlights research that remains central to developments today in particle physics, quantum field and string theory, gravitation, cosmology, and particle astrophysics.