Center for Theoretical Physics of the Universe (CTPU)

An introduction to decomposition

by Eric Sharpe (Virginia Tech)

zoom meeting

zoom meeting


In this talk I will review work on `decomposition,' a property of 2d 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 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 generalizations of spaces, decomposition has been the driver of a number of developments since. As time permits, I will illustrate with examples in finite gauge theories, and describe the recent application there to the anomaly resolution procedure of Wang-Wen-Witten.