Decomposition and (Non-Invertible) (-1)-Form Symmetries from the Symmetry Topological Field Theory

Abstract: We investigate the interplay between (-1)-form symmetries and their quantum-dual (d-1)-form counterparts within the framework of Symmetry Topological Field Theories (SymTFTs). In this framework the phenomenon of decomposition -- a d-dimensional quantum field theory with (d-1)-form symmetry being the disjoint union of other theories (or ''universes'') -- arises naturally from manipulations of topological boundary conditions of the SymTFT. We corroborate our findings with various examples, including a generalization of ''instanton-restricted'' 4d Yang-Mills theories with no sum over instanton sectors. Furthermore, we construct a 3d SymTFT with a non-invertible (-1)-form symmetry. The absolute 2d quantum field theory includes a 0-form global symmetry that depends on a parameter whose value gets shifted by the action of the (-1)-form symmetry, and we show that the non-invertibility of the latter is needed to encode this modification of the 0-form symmetry.