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On gauging symmetry of modular categories

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OASW01 - Structure of operator algebras: subfactors and fusion categories

Co-authors: Shawn X. Cui ( Stanford University), César Galindo (Universidad de los Andes), Zhenghan Wang (Microsoft Research, Station QUniversity of CaliforniaSanta Barbara)
 
A very interesting class of fusion categories is the one formed by modular categories. These categories arise in a variety of mathematical subjects including topological quantum field theory, conformal field theory, representation theory of quantum groups, von Neumann algebras, and vertex operator algebras. In addition to the mathematical interest, a motivation for pursuing a classification of modular categories comes from their application in condensed matter physics and quantum computing.
 
Gauging is a well-known theoretical tool to promote a global symmetry to a local gauge symmetry. In this talk, we will present a mathematical formulation of gauging in terms of higher category formalism. Roughly, given a unitary modular category (UMC) with a symmetry group G, gauging is a 2-step process: first extend the UMC to a G-crossed braided fusion category and then take the equivariantization of the resulting category. This is an useful tool to construct new modular categories from given ones. We will show through concrete examples which are the ingredients involved in this process. In addition, if time allows, we will mention some classification results and conjectures associated to the notion of gauging. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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