Abstract
Phys.Rev.D83:084019,2011 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 $\Z_p$ gauge theories shows that they are associated
with an emergent $\Z_p$ 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.