# Entanglement entropy and superselection sectors I. Global symmetries

## TL;DR

This paper explores how superselection sectors from global symmetries affect entanglement entropy in quantum field theories, highlighting differences from duality and additivity loss, with implications for holography.

## Contribution

It provides a detailed review of superselection sectors related to global symmetries and their impact on entanglement entropy, connecting mathematical structures to physical phenomena.

## Key findings

- Superselection sectors influence entanglement entropy calculations.
- Models with finite and Lie group symmetries exhibit distinct entropy features.
- Holographic entanglement entropy may correspond to a sub-theory with many superselection sectors.

## Abstract

Some quantum field theories show, in a fundamental or an effective manner, an alternative between a loss of duality for algebras of operators corresponding to complementary regions, or a loss of additivity. In this latter case, the algebra contains some operator that is not generated locally, in the former, the entropies of complementary regions do not coincide. Typically, these features are related to the incompleteness of the operator content of the theory, or, in other words, to the existence of superselection sectors. We review some aspects of the mathematical literature on superselection sectors aiming attention to the physical picture and focusing on the consequences for entanglement entropy (EE). For purposes of clarity, the whole discussion is divided into two parts according to the superselection sectors classification: The present part I is devoted to superselection sectors arising from global symmetries, and the forthcoming part II will consider those arising from local symmetries. Under this perspective, here restricted to global symmetries, we study in detail different cases such as models with finite and Lie group symmetry as well as with spontaneous symmetry breaking or excited states. We illustrate the general results with simple examples. As an important application, we argue the features of holographic entanglement entropy correspond to a picture of a sub-theory with a large number of superselection sectors and suggest some ways in which this identification could be made more precise.