Non-abelian 3D bosonization and quantum Hall states

Ðorđe Radičević,David Tong,Carl Turner

doi:10.1007/jhep12(2016)067

Ðorđe Radičević, David Tong + Show 1 more

Open Access

https://doi.org/10.1007/jhep12(2016)067

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Abstract

Bosonization dualities relate two different Chern-Simons-matter theories, with bosonic matter on one side replaced by fermionic matter on the other. We first describe a more general class of non-Abelian bosonization dualities. We then explore the non-relativistic physics of these theories in the quantum Hall regime. The bosonic theory lies in a condensed phase and admits vortices which are known to form a non-Abelian quantum Hall state. We ask how this same physics arises in the fermionic theory. We find that a condensed boson corresponds to a fully filled Landau level of fermions, while bosonic vortices map to fermionic holes. We confirm that the ground state of the two theories is indeed described by the same quantum Hall wavefunction.

Highlights

In this paper, our interest lies in the non-Abelian versions of the bosonization dualities
We explore the nonrelativistic physics of these theories in the quantum Hall regime
There are a bewildering number of descriptions of quantum Hall states

Summary

The bosonic theory

The direct method is to construct the quantum mechanics of M vortices and solve for its ground state wavefunction. This involves solving a complicated many-body system and, in general, is not easy. For a more indirect method, recall that the gauge group is unbroken inside the droplet of vortices, but broken outside This means that the low-energy dynamics includes a U(N )k, k Chern-Simons theory which, on the edge of the droplet, induces a U(N )k, k WZW conformal field theory. A much more direct approach is as follows: determine the interactions between vortices and solve for the ground state wavefunction Both of these steps are difficult and in general there is no reason to believe that this is any easier than other many-body problems. In the large N limit, the dynamics of these excitations can be shown to coincide with those of the U(N )k, k WZW conformal field theory [39]

The fermionic theory

Discussion