Non-abelian 3$D$ bosonization and quantum Hall states
Published version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Radičević, Ð
Tong, David https://orcid.org/0000-0001-9120-2174
Turner, Carl https://orcid.org/0000-0001-7202-5731
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.
Description
Keywords
Chern-Simons theories, duality in gauge field theories, field theories in lower dimensions, topological states of matter
Journal Title
Journal of High Energy Physics
Conference Name
Journal ISSN
1126-6708
1029-8479
1029-8479
Volume Title
2016
Publisher
Springer
Publisher DOI
Sponsorship
Science and Technology Facilities Council (ST/L000385/1)
DT thanks Stanford SITP for their kind hospitality while this work was initiated. DT and CT are supported by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013), ERC grant agreement STG 279943, “Strongly Coupled Systems”, and CT is also supported by an STFC studentship. ÐR is supported by a Stanford Graduate Fellowship and thanks the Perimeter Institute for hospitality while this work was being finished. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development & Innovation.