Symmetry TFTs for Non-Invertible Defects

Understand

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.