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$2D-$ Fractional Supersymmetry and Conformal Field Theory for alternative statistics
High Energy Physics - Theory · Submitted 28 Jun 1996
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The creation and annihilation operators turn out to generate alternative statistics, currently referred as quons in the literature.
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The abstract, sentence by sentence
Supersymmetry can be consistently generalized in one and two dimensional spaces, fractional supersymmetry being one of the possible extension. 2D fractional supersymmetry of arbitrary order $F$ is explicitly constructed using an adapted superspace formalism. This symmetry connects the fractional spin states ($0,{1 \over F}, ...,{F-1 \over F}$). Besides the stress momentum tensor, we obtain a conserved current of spin($1 + {1 \over F})$. The coherence of the theory imposes strong constraints upon the commutation relations of the modes of the fields. The creation and annihilation operators turn out to generate alternative statistics, currently referred as quons in the literature. We consider, with a special attention, the consistence of the algebra, on the level of the Hilbert space and the Green functions. The central charges are generally irrational numbers except for the particular cases $F=2,3,4$. A natural classification emerges according to the decomposition of $F$ into its product of prime numbers leading to sub-systems with smaller symmetries.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Supersymmetry can be consistently generalized in one and two dimensional spaces, fractional supersymmetry being one of the possible extension. 2D fractional supersymmetry of arbitrary order $F$ is explicitly constructed using an adapted superspace formalism. | contribution 0.72 | 0.74 | 0.15 | asserted 0.90 |
| s1 | This symmetry connects the fractional spin states ($0,{1 \over F}, ...,{F-1 \over F}$). | result 0.87 | 0.66 | 0.11 | asserted 1.00 |
| s2 | Besides the stress momentum tensor, we obtain a conserved current of spin($1 + {1 \over F})$. | result 0.98 | 0.91 | 0.09 | asserted 1.00 |
| s3 | The coherence of the theory imposes strong constraints upon the commutation relations of the modes of the fields. | result 0.72 | 0.66 | 0.09 | asserted 1.00 |
| s4 | The creation and annihilation operators turn out to generate alternative statistics, currently referred as quons in the literature. | result 0.90 | 0.86 | 0.30 | asserted 1.00 |
| s5 | We consider, with a special attention, the consistence of the algebra, on the level of the Hilbert space and the Green functions. | contribution 0.87 | 0.87 | 0.07 | asserted 0.54 |
| s6 | The central charges are generally irrational numbers except for the particular cases $F=2,3,4$. | result 1.00 | 0.82 | 0.12 | asserted 0.99 |
| s7 | A natural classification emerges according to the decomposition of $F$ into its product of prime numbers leading to sub-systems with smaller symmetries. | result 0.74 | 0.80 | 0.14 | asserted 0.99 |
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Original abstract
Supersymmetry can be consistently generalized in one and two dimensional spaces, fractional supersymmetry being one of the possible extension. 2D fractional supersymmetry of arbitrary order $F$ is explicitly constructed using an adapted superspace formalism. This symmetry connects the fractional spin states ($0,{1 \over F}, ...,{F-1 \over F}$). Besides the stress momentum tensor, we obtain a conserved current of spin($1 + {1 \over F})$. The coherence of the theory imposes strong constraints upon the commutation relations of the modes of the fields. The creation and annihilation operators turn out to generate alternative statistics, currently referred as quons in the literature. We consider, with a special attention, the consistence of the algebra, on the level of the Hilbert space and the Green functions. The central charges are generally irrational numbers except for the particular cases $F=2,3,4$. A natural classification emerges according to the decomposition of $F$ into its product of prime numbers leading to sub-systems with smaller symmetries.
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2 arXiv papers cite this in 2 sentences
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Low dimensional field theories, in particular conformal field theories, have also been discussed [ref] and a generalization of the Virasoro algebra has been discovered [ref] .
On Linear Differential Equations Involving a Para-Grassmann Variable · Introduction · 0.93
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