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Fractional Superspace Formulation of Generalized Super-Virasoro Algebras

Stephane Durand
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Abstract

We present a fractional superspace formulation of the centerless parasuper-Viraso-ro and fractional super-Virasoro algebras. These are two different generalizations of the ordinary super-Virasoro algebra generated by the infinitesimal diffeomorphisms of the superline. We work on the fractional superline parametrized by $t$ and $θ$, with $t$ a real coordinate and $θ$ a paragrassmann variable of order $M$ and canonical dimension $1/F$. We further describe a more general structure labelled by $M$ and $F$ with $M\geq F$. The case $F=2$ corresponds to the parasuper-Virasoro algebra of order $M$, while the case $F=M$ leads to the fractional super-Virasoro algebra of order $F$. The ordinary super-Virasoro algebra is recovered at $F=M=2$. The connection with $q$-oscillator algebras is discussed.

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Stephane Durand. 1992-06-26. Fractional Superspace Formulation of Generalized Super-Virasoro Algebras. https://doi.org/10.1142/s0217732392002275

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