Classical and quantum N=1 super $W_\infty$-algebras

TL;DR

This paper constructs higher-spin N=1 super algebras extending the super Virasoro algebra, identifies two classical Poisson structures, and determines that only one can be consistently quantized.

Contribution

It introduces two classical superalgebras with higher spins and analyzes their quantization viability, revealing a unique consistent quantum algebra.

Findings

Two distinct classical superalgebras identified

Only one classical algebra admits consistent quantization

Extension of super Virasoro algebra to all spins s ≥ 3/2

Abstract

We construct higher-spin N=1 super algebras as extensions of the super Virasoro algebra containing generators for all spins $s\ge 3/2$. We find two distinct classical (Poisson) algebras on the phase super space. Our results indicate that only one of them can be consistently quantized.