Generalized charges, part II: Non-invertible symmetries and the symmetry TFT

Journal article

Consider a dd-dimensional quantum field theory (QFT) \mathfrak{T}𝔗, with a generalized symmetry \mathcal{S}𝒮, which may or may not be invertible. We study the action of \mathcal{S}𝒮 on generalized or qq-charges, i.e. qq-dimensional operators. The main result of this paper is that qq-charges are characterized in terms of the topological defects of the Symmetry Topological Field Theory (SymTFT) of \mathcal{S}𝒮, also known as the “Sandwich Construction”. The SymTFT is a (d+1)(d+1)-dimensional topological field theory, which encodes the symmetry \mathcal{S}𝒮 and the physical theory in terms of its boundary conditions. Our proposal applies quite generally to any finite symmetry \mathcal{S}𝒮, including non-invertible, categorical symmetries. Mathematically, the topological defects of the SymTFT form the Drinfeld Center of the symmetry category \mathcal{S}𝒮. Applied to invertible symmetries, we recover the result of Part I of this series of papers. After providing general arguments for the identification of qq-charges with the topological defects of the SymTFT, we develop this program in detail for QFTs in 2d (for general fusion category symmetries) and 3d (for fusion 2-category symmetries).

Authors: Bhardwaj, L; Schäfer-Nameki, S

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: SciPost
• Journal: SciPost Physics
• Volume: 19
• Issue: 4
• Article number: 098
• Publication date: 2025-10-15
• Acceptance date: 2025-09-15
• DOI: 10.21468/scipostphys.19.4.098
• EISSN: 2542-4653
• ISSN: 2542-4653
• Language: English