Symmetries and Strings in Field Theory and Gravity

Abstract

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 ${\mathbb{Z}}_p$ one-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.

45 pages, minor changes

References in corpus (8)

• CFT Duals for Extreme Black Holes
• Topological boundary conditions in abelian Chern-Simons theory
• Comments on the Fayet-Iliopoulos Term in Field Theory and Supergravity
• Notes on gauging noneffective group actions
• Classification of abelian spin Chern-Simons theories
• Variant supercurrent multiplets
• Quantization of Fayet-Iliopoulos Parameters in Supergravity
• Variant supercurrents and Noether procedure

Cited by in corpus (3)

• A Supersymmetric One Higgs Doublet Model
• TASI Lectures on Supergravity and String Vacua in Various Dimensions
• Number-Theory Dark Matter