On Superconformal Anyons
arXiv:1511.01491 · doi:10.1007/JHEP01(2016)138
Abstract
In d=2+1 dimensions, there exist field theories which are non-relativistic and superconformal. These theories describe two species of anyons, whose spins differ by 1/2, interacting in a harmonic trap. We compute the dimensions of chiral primary operators. These operators receive large anomalous dimensions which are related to the unusual angular momentum properties of anyons. Surprisingly, we find that the dimensions of some chiral primary operators violate the unitarity bound and we trace this to the fact that the associated wavefunctions become non-normalisable. We also study BPS non-perturbative states in this theory: these are Jackiw-Pi vortices. We show that these emerge at exactly the point where perturbative operators hit the unitarity bound. To describe the low-energy dynamics of these vortices, we construct a novel type of supersymmetric gauged linear sigma model.
32 pages + appendix, 3 figures (plus Feynman diagrams drawn with feynMF). v2: references added. v3 typos corrected, version to appear in JHEP
References in corpus (4)
Cited by in corpus (11)
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- Renormalization properties of a Galilean Wess-Zumino model
- Rigid Supersymmetric Backgrounds of 3-dimensional Newton-Cartan Supergravity
- The Conformal Spectrum of Non-Abelian Anyons
- Two-dimensional Schrödinger symmetry and three-dimensional breathers and Kelvin-ripple complexes as quasi-massive-Nambu-Goldstone modes
- Massive Nambu-Goldstone Fermions and Bosons for Non-relativistic Superconformal Symmetry: Jackiw-Pi Vortices in a Trap
- The Quantum Origins of Non-Topological Vortices