Symmetries and Strings in Field Theory and Gravity

TL;DR

This paper explores the role of discrete and gauge symmetries in quantum field theory and gravity, revealing new phenomena, observables, and a unified perspective on symmetry constraints in supergravity.

Contribution

It provides a unified framework for understanding discrete gauge symmetries, emergent gauge symmetries, and their implications for quantum gravity and supergravity consistency conditions.

Findings

Discrete gauge theories relate to emergent one-form gauge symmetries.

New observables and phenomena in nonlinear sigma-models are identified.

Supports the conjecture that quantum gravity lacks global symmetries and all gauge charges are present.

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 $\Z_p$ 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.