Symmetry TFTs for Non-Invertible Defects

Abstract

Given any symmetry acting on a $d$-dimensional quantum field theory, there is an associated $(d+1)$-dimensional topological field theory known as the Symmetry TFT (SymTFT). The SymTFT is useful for decoupling the universal quantities of quantum field theories, such as their generalized global symmetries and 't Hooft anomalies, from their dynamics. In this work, we explore the SymTFT for theories with Kramers-Wannier-like duality symmetry in both $(1+1)$d and $(3+1)$d quantum field theories. After constructing the SymTFT, we use it to reproduce the non-invertible fusion rules of duality defects, and along the way we generalize the concept of duality defects to \textit{higher} duality defects. We also apply the SymTFT to the problem of distinguishing intrinsically versus non-intrinsically non-invertible duality defects in $(1+1)$d.

119 pages, 46 figures; v2: references added, typos corrected; v3: publication version

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