2023/05/26 by Lakshya Bhardwaj, Bhardwaj, Lakshya, Sakura Schäfer‐Nameki +1 · 14 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Category Theory (math.CT) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Origins and Evolution of Life #Quantum Algebra (math.QA) #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.2305.17159
openalex publication_date 2023/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Consider a d-dimensional quantum field theory (QFT) \mathfrakT, with a generalized symmetry S, which may or may not be invertible. We study the action of S on generalized or q-charges, i.e. q-dimensional operators. The main result of this paper is that q-charges are characterized in terms of the topological defects of the Symmetry Topological Field Theory (SymTFT) of S, also known as the ``Sandwich Construction''. The SymTFT is a (d+1)-dimensional topological field theory, which encodes the symmetry S and the physical theory in terms of its boundary conditions. Our proposal applies quite generally to any finite symmetry S, including non-invertible, categorical symmetries. Mathematically, the topological defects of the SymTFT form the Drinfeld Center of the symmetry category 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 q-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).