Spinon bases in supersymmetric CFT's
In: Journal of Physics. A, Mathematical and Theoretical, Jg. 49 (2016)
Online
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Zugriff:
We present a novel way to organise the finite size spectra of a class of conformal field theories (CFT) with $\mathcal{N}=2$ or (non-linear) $\mathcal{N}=4$ superconformal symmetry. Generalising the spinon basis of the $SU(n)_1$ WZW theories, we introduce supersymmetric spinons $(\phi^-, \phi^{+})$, which form a representation of the supersymmetry algebra. In each case, we show how to construct a multi-spinon basis of the chiral CFT spectra. The multi-spinon states are labelled by a collection $\{ n_j \}$ of (discrete) momenta. The state-content for given choice of $\{ n_j \}$ is determined through a generalised exclusion principle, similar to Haldane's `motif' rules for the $SU(n)_1$ theories. In the simplest case, which is the ${\cal N}=2$ superconformal theory with central charge $c=1$, we develop an algebraic framework similar to the Yangian symmetry of the $SU(2)_1$ theory. It includes an operator $H_2$, akin to a CFT Haldane-Shastry Hamiltonian, which is diagonalised by multi-spinon states. In all cases studied, we obtain finite partition sums by capping the spinon-momenta to some finite value. For the $\mathcal{N}=2$ superconformal CFTs, this finitisation precisely leads to the so-called M$_k$ supersymmetric lattice models with characteristic order-$k$ exclusion rules on the lattice. Finitising the $c=2$ CFT with non-linear ${\cal N}=4$ superconformal symmetry similarly gives lattice model partition sums for spin-full fermions with on-site and nearest neighbour exclusion.
Comment: 36 pages, 3 figures
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Spinon bases in supersymmetric CFT's
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Autor/in / Beteiligte Person: | Fokkema, Thessa ; Schoutens, Kareljan ; Quantum Condensed Matter Theory (ITFA, IoP, FNWI) |
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Zeitschrift: | Journal of Physics. A, Mathematical and Theoretical, Jg. 49 (2016) |
Veröffentlichung: | IOP Publishing Ltd., 2016 |
Medientyp: | unknown |
ISSN: | 1751-8121 (print) ; 1751-8113 (print) |
DOI: | 10.1088/1751-8113/49/28/285004 |
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