The Topological Equivalence Principle: On Decoupling TFTs from Gravity

TL;DR

This paper investigates the relationship between topological field theories and gravity, revealing that TFT sectors are sensitive to gravitational effects and are thus incompatible with consistent quantum gravity theories, placing them in the Swampland.

Contribution

It introduces the Topological Equivalence Principle, showing that TFTs cannot be decoupled from gravity and are non-topological in the presence of dynamical gravity, challenging their role in quantum systems.

Findings

TFT sectors are non-perturbatively sensitive to Newton's constant.

Topological operators become non-topological in gravitational duals.

TFTs are in the Swampland, incompatible with quantum gravity.

Abstract

Topological field theories (TFTs) play an important role in characterizing the deep infrared (IR) of many quantum systems with a mass gap, as well as the global symmetries of quantum field theories (QFTs) decoupled from gravity. In gravitational asymptotically AdS spacetimes, TFT sectors which are putatively decoupled from local metric data are nevertheless non-perturbatively sensitive to Newton's constant via a sum over topologically distinct saddle point configurations. Tracking the fate of this non-decoupling in the boundary dual, we argue that in spite of appearances, this dependence on Newton's constant extends to local metric fluctuations. Said differently, TFTs are in the Swampland. In tandem with earlier results on the absence of global symmetries in theories with subregion-subregion duality, this also establishes that topological operators of boundary systems with a gravity dual are always non-topological in the bulk.