Symmetry Operators and 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.

8 pages including references. v2: Corrected typos and made minor clarifications to discussion

References in corpus (7)

• Generalized Global Symmetries
• Symmetries and Strings in Field Theory and Gravity
• TASI Lectures on Solitons
• Branes and Non-Invertible Symmetries
• On the Holographic Dual of a Topological Symmetry Operator
• Generalized Symmetries, Gravity, and the Swampland
• $U(1)$ $R$-Symmetry Topological Operators from Branes in Holography

Cited by in corpus (2)

• Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment
• Non-invertible symmetries of two-dimensional Non-Linear Sigma Models