Treelike structure of symmetry topological field theories and multisector QFTs

Abstract

The global symmetries of a D - dimensional quantum field theory (QFT) can, in many cases, be captured in terms of a ( D + 1) -dimensional symmetry topological field theory (SymTFT). In this work we construct a ( D + 1) -dimensional theory which governs the symmetries of QFTs with multiple sectors which have connected correlators that admit a decoupling limit. The associated symmetry field theory decomposes into a SymTree, namely a treelike structure of SymTFTs fused along possibly nontopological junctions. In string -realized multisector QFTs, these junctions are smoothed out in the extradimensional geometry, as we demonstrate in examples. We further use this perspective to study the fate of higher -form symmetries in the context of holographic large M averaging where the topological sectors of different large M replicas become dressed by additional extended operators associated with the SymTree.