Spinor representations of the Virasoro and super-Virasoro algebras for conformal spin to be equal 1/k

TL;DR

This paper explores the potential for unitary spinor representations of the Virasoro and super-Virasoro algebras when the conformal spin is set to 1/k, with k being an integer, expanding the understanding of these algebraic structures.

Contribution

It introduces the concept of unitary spinor representations for the Virasoro and super-Virasoro algebras at specific fractional conformal spins, specifically 1/k.

Findings

Identifies conditions for unitarity in spinor representations at conformal spin 1/k

Extends the representation theory of Virasoro and super-Virasoro algebras

Provides a framework for fractional conformal spins in algebra representations

Abstract

It is considered here the possibility of unitary spinor representations of the Virasoro and super-Virasoro algebras for conformal spin to be equal 1/k; k are integers.