Speaker: Kantaro Ohmori (U. Tokyo)
Title: Higher Representation Theory for Excitations
Abstract: In this talk, I will present a framework for understanding the representation theory of excitations in gapped phases of quantum field theories. This depends on both the microscopic symmetries of the system and its macroscopic phase. We introduce the strip algebra, an extension of the tube algebra, to define this representation theory. The representation theory of the strip algebra is tractable because it is equivalent to the dual category of the system's symmetry category in terms of a module.
In 1+1 dimensions, applying our framework to systems with non-invertible symmetries predicts degeneracies between solitons and particles and introduces selection rules in terms of multiplets. In higher dimensions, we define the strip algebra within the context of higher linear algebra, leading to a higher representation theory that describes both particle-like and extended excitations, such as strings.
We apply this framework to gauge theories and find that it reproduces expected results. For example, in a deconfined gapped phase, the representation theory includes quark excitations, while in a confined phase, only baryons appear. This demonstrates how the abelian part of the gauge charge can be reconstructed from information about the phase.
This talk will be based on arXiv:2408.11045 , which is joint work with Clay Cordova and Nicholas Holfester, and arXiv:2501.09069 , which is joint work with Finn Gagliano and Andrea Grigoletto.
Note unusual time: 2:30 pm GMT