An introduction to decomposition


Sharpe, E. (2022). An introduction to decomposition. Perimeter Institute. https://pirsa.org/22010077


Sharpe, Eric. An introduction to decomposition. Perimeter Institute, Jan. 11, 2022, https://pirsa.org/22010077


          @misc{ pirsa_22010077,
            doi = {10.48660/22010077},
            url = {https://pirsa.org/22010077},
            author = {Sharpe, Eric},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {An introduction to decomposition},
            publisher = {Perimeter Institute},
            year = {2022},
            month = {jan},
            note = {PIRSA:22010077 see, \url{https://pirsa.org}}

Eric Sharpe Virginia Polytechnic Institute and State University


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 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.