Solitonic symmetry as non-invertible symmetry: cohomology theories with TQFT coefficients

Understand

Originating from the topology of the path-integral target space $Y$, solitonic symmetry describes the conservation law of topological solitons and the selection rule of defect operators.

• As Ref.~\cite{Chen:2022cyw} exemplifies, the conventional treatment of solitonic symmetry as an invertible symmetry based on homotopy groups is inappropriate.
• In this paper, we develop a systematic framework to treat solitonic symmetries as non-invertible generalized symmetries.
• We propose that the non-invertible solitonic symmetries are generated by the partition functions of auxiliary topological quantum field theories (TQFTs) coupled with the target space $Y$.