SciPost Phys. 7, 007 (2019) ·
published 10 July 2019

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We describe a web of wellknown dualities connecting quantum field theories
in $d=1+1$ dimensions. The web is constructed by gauging ${\bf Z}_2$ global
symmetries and includes a number of perennial favourites such as the
JordanWigner transformation, KramersWannier duality, bosonization of a Dirac
fermion, and Tduality. There are also lessloved examples, such as nonmodular
invariant $c=1$ CFTs that depend on a background spin structure.
SciPost Phys. 4, 022 (2018) ·
published 30 April 2018

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We study the spectrum of multiple nonAbelian anyons in a harmonic trap. The
system is described by ChernSimons theory, coupled to either bosonic or
fermionic nonrelativistic matter, and has an SO(2,1) conformal invariance. We
describe a number of special properties of the spectrum, focussing on a class
of protected states whose energies are dictated by their angular momentum. We
show that the angular momentum of a bound state of nonAbelian anyons is
determined by the quadratic Casimirs of their constituents.