From physical symmetries to emergent gauge symmetries

TL;DR

This paper explores how gauge symmetries can emerge in field theories without fundamental gauge invariance, focusing on abelian theories and the role of Noether currents, with implications for emergent gravity.

Contribution

It provides a systematic analysis of the emergence of gauge symmetries from trivialized Noether currents in abelian field theories, including detailed examples and connections to emergent gravity.

Findings

Emergent gauge symmetries arise from decoupled degrees of freedom.

Explicit example of vector field theory illustrates the mechanism.

Discussion of implications for the emergent gravity program and Weinberg-Witten theorem.

Abstract

Gauge symmetries indicate redundancies in the description of the relevant degrees of freedom of a given field theory and restrict the nature of observable quantities. One of the problems faced by emergent theories of relativistic fields is to understand how gauge symmetries can show up in systems that contain no trace of these symmetries at a more fundamental level. In this paper we start a systematic study aimed to establish a satisfactory mathematical and physical picture of this issue, dealing first with abelian field theories. We discuss how the trivialization, due to the decoupling and lack of excitation of some degrees of freedom, of the Noether currents associated with physical symmetries leads to emergent gauge symmetries in specific situations. An example of a relativistic field theory of a vector field is worked out in detail in order to make explicit how this mechanism works and to clarify the physics behind it. The interplay of these ideas with well-known results of importance to the emergent gravity program, such as the Weinberg-Witten theorem, are discussed.