2023/06/20 by Lawrie, Craig, Yu, Xingyang, Zhang, Hao Y. · 3 citations
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2306.11783
Within the framework of relative and absolute quantum field theories (QFTs), we present a general formalism for understanding polarizations of the intermediate defect group and constructing non-invertible duality defects in theories in 2k spacetime dimensions with self-dual gauge fields. We introduce the polarization pair, which fully specifies absolute QFTs as far as their (k-1)-form defect groups are concerned, including their (k-1)-form symmetries, global structures (including discrete θ-angle), and local counterterms. Using the associated symmetry TFT, we show that the polarization pair is capable of succinctly describing topological manipulations, e.g., gauging (k-1)-form global symmetries and stacking counterterms, of absolute QFTs. Furthermore, automorphisms of the (k-1)-form charge lattice naturally act on polarization pairs via their action on the defect group; they can be viewed as dualities between absolute QFTs descending from the same relative QFT. Using this formalism, we present a prescription for building non-invertible symmetries of absolute QFTs. A large class of known examples, e.g., non-invertible defects in 4D N=4 super-Yang--Mills, can be reformulated via this prescription. As another class of examples, we identify and investigate in detail a family of non-invertible duality defects in 6D superconformal field theories (SCFTs), including from the perspective of the symmetry TFT derived from Type IIB string theory.