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The Department of Mathematics is a bustling place full of new ideas. We host several events that occur throughout the year, including seminars, colloquium, conferences, and social events. Our seminars and colloquium are open to the public: all students, faculty, or alumni who are interested are welcome to join us for exciting talks on the leading edge of mathematics research!

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Math/Physics Seminar: An Introduction to Decomposition

Event Type
Seminar/Symposium
Sponsor
n/a
Virtual
wifi event
Date
Feb 3, 2022   1:00 pm  
Speaker
Eric Sharpe, Virginia Tech
Contact
Sheldon Katz
E-Mail
katzs@illinois.edu
Views
43

Abstract: 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.

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