Title: An Introduction to Fusion Rings
Abstract: Fusion rings turn up in various places in physics and mathematics.
They are very simple mathematical structures describing generalized
addition of charges. Nevertheless, they generalize finite groups and
even making a comprehensive list of small examples is hard. Given a
fusion ring, one may ask if there are more intricate and useful
structures compatible with it. For example, is there a tensor category
or even a modular tensor category with the same fusion rules? In that
case the fusion ring is associated with a model of particles in 1+1D
or 2+1D with topological interactions.
I will introduce fusion rings assuming no prior knowledge, discuss how
one may try to find them (with help from a computer), and how to then
try and find the corresponding category structures. I hope to give
some interesting examples, including rings with non-Abelian fusion and
to discuss applications to particles braiding on wire networks.
Talk – Video I
Talk – Video II
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Last Updated: 26th September 2022 by George Rogers
Joost Slingerland (Maynooth University)
Title: An Introduction to Fusion Rings
Abstract: Fusion rings turn up in various places in physics and mathematics.
They are very simple mathematical structures describing generalized
addition of charges. Nevertheless, they generalize finite groups and
even making a comprehensive list of small examples is hard. Given a
fusion ring, one may ask if there are more intricate and useful
structures compatible with it. For example, is there a tensor category
or even a modular tensor category with the same fusion rules? In that
case the fusion ring is associated with a model of particles in 1+1D
or 2+1D with topological interactions.
I will introduce fusion rings assuming no prior knowledge, discuss how
one may try to find them (with help from a computer), and how to then
try and find the corresponding category structures. I hope to give
some interesting examples, including rings with non-Abelian fusion and
to discuss applications to particles braiding on wire networks.
Talk – Video I
Talk – Video II
Category: Uncategorised
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