Super Gelfand-Dickey Algebra And Integrable Models

TL;DR

This paper systematically explores integrable models and supersymmetric extensions of the Gelfand-Dickey algebra, detailing their relation to super pseudo-differential operators and conformal algebra extensions.

Contribution

It introduces a comprehensive analysis of supersymmetric Gelfand-Dickey algebra and its connection to super pseudo-differential operators and conformal algebra extensions.

Findings

Established the relation between super pseudo-differential operators and conformal algebra extensions

Developed a framework for supersymmetric integrable models based on Gelfand-Dickey algebra

Provided detailed descriptions of higher and lower spin extensions

Abstract

We present in this work a systematic study of integrable models and supersymmetric extensions of the Gelfand-Dickey algebra of pseudo differential operators. We describe in detail the relation existing between the algebra of super pseudo-differential operators on the ring of superfields $u_{\frac{s}{2}}(z,\theta),s\in Z$ and the higher and lower spin extensions of the conformal algebra.