The Calogero Model and the Virasoro Symmetry

TL;DR

This paper develops new realizations of the Virasoro algebra inspired by the Calogero model, including superextensions and higher-spin $W_ abla$-type algebras, revealing their spectrum-generating properties.

Contribution

It introduces novel realizations of the Virasoro algebra based on the Calogero model, along with superextensions and higher-spin extensions of the $W_ abla$ type.

Findings

Virasoro algebra acts as spectrum-generating algebra for the Calogero model

Constructed superextended Virasoro algebra realizations

Introduced higher-spin $W_ abla$-type extensions of the Virasoro algebra

Abstract

We construct new realizations of the Virasoro algebra inspired by the Calogero model. The Virasoro algebra we find acts as a kind of spectrum-generating algebra of the Calogero model. We furthermore present the superextension of these results and introduce a class of higher-spin extensions of the Virasoro algebra which are of the $W_\infty$ - type.