Symmetry Operators and Gravity

TL;DR

This paper explores how the presence of gravity affects the nature of topological symmetry operators, showing that gravity prevents their existence by making the zero-width limit ill-defined.

Contribution

It introduces the idea that gravitational effects hinder the formation of ideal topological operators by regularization issues and fluctuation effects.

Findings

Regularized symmetry operators have finite tension and fluctuate.

Gravity renders the zero-width limit of these operators ill-defined.

Topological operators cannot exist in the presence of gravity.

Abstract

We argue that topological operators for continuous symmetries written in terms of currents need regularization, which effectively gives them a small but finite width. The regulated operator is a finite tension object which fluctuates. In the zero-width limit these fluctuations freeze, recovering the properties of a topological operator. When gravity is turned on, the zero-width limit becomes ill-defined, thereby prohibiting the existence of topological operators.