Symmetry Operators and Gravity
Ibrahima Bah, Patrick Jefferson, Konstantinos Roumpedakis, Thomas Waddleton
TL;DR
This work analyzes whether topological operators measuring charges for continuous symmetries survive when gravity is turned on. The authors model symmetry insertions as regulated solitons with finite width $\lambda$, yielding a worldvolume theory for the defect's Goldstone modes and an effective tension $T_{\rm eff}$ that typically scales as $1/\lambda$, ensuring the topological operator emerges only in the strict zero-width limit. When gravity is present, however, graviton couplings generate tadpole terms that make $T_{\rm eff}$ diverge as $\lambda \to 0$, preventing the Goldstone modes from freezing and hence obstructing the existence of topological operators. This gravity-induced obstruction suggests that in quantum gravity there is no conventional operator measuring a conserved charge, with potential implications for symmetry realization, defect dynamics, and holographic perspectives. The results motivate further exploration of regulated defects across discrete, higher-form, and categorical symmetries, as well as connections to AdS/CFT and possible bounds on charge measurement uncertainty in gravitational settings.
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.