In this talk I will review work on `decomposition,' a property of 2d quantum field theories with 1-form symmetries and, more generally, d-dim'l theories with (d-1)-form symmetries. Decomposition is the observation that such quantum field theories are equivalent to ('decompose into’) disjoint unions of other QFTs, known in this context as "universes.”
Examples include two-dimensional gauge theories and orbifolds with matter invariant under a subgroup of the gauge group. Decomposition explains and relates several physical properties of these theories -- for example, restrictions on allowed instantons arise as a "multiverse interference effect" between contributions from constituent universes. First worked out in 2006 as part of efforts to understand string propagation on stacks, decomposition has been the driver of a number of developments since. In the first half of this talk, I will review decomposition; in the second half, I will focus on the recent application to anomaly resolution of Wang-Wen-Witten in two-dimensional orbifolds.
