Effective Theories for 2+1 Dimensional Non-Abelian Topological Spin Liquids

Abstract

In this work we propose an effective low-energy theory for a large class of 2+1 dimensional non-Abelian topological spin liquids whose edge states are conformal degrees of freedom with central charges corresponding to the coset structure $su(2{)}_k\oplus su(2{)}_{k^{\prime }}/su(2{)}_{k+k^{\prime }}$. For particular values of $k^{\prime }$ it furnishes the series for unitary minimal and superconformal models. These gapped phases were recently suggested to be obtained from an array of one-dimensional coupled quantum wires. In doing so we provide an explicit relationship between two distinct approaches: quantum wires and Chern-Simons bulk theory. We firstly make a direct connection between the interacting quantum wires and the corresponding conformal field theory at the edges, which turns out to be given in terms of chiral gauged WZW models. Relying on the bulk-edge correspondence we are able to construct the underlying non-Abelian Chern-Simons effective field theory.

arXiv comment41 pages, 5 figures, typos corrected, references added, published version

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Cited by in corpus (5)

• Coupled-wire constructions: a Luttinger liquid approach to topology
• From Quantum Wires to the Chern-Simons Description of the Fractional Quantum Hall Effect
• Quantum wires, Chern-Simons theory, and dualities in the quantum Hall system
• Bosonization, Duality, and the $C$-Theorem in the Non-Abelian Thirring Model
• Chiral Edge States in 2+1 Dimensional Topological Phases