A spinor-like representation of the contact superconformal algebra K'(4)

TL;DR

This paper constructs an embedding of a central extension of the contact superconformal algebra K'(4) into pseudodifferential symbols, revealing a new family of simplified spinor-like representations with fewer fields.

Contribution

It introduces a novel embedding of K'(4) into pseudodifferential symbols and uncovers a one-parameter family of reduced spinor-like representations.

Findings

Embedded K'(4) into pseudodifferential symbols on supercircle

Discovered a one-parameter family of 4-field irreducible representations

Reduced the number of fields needed for representations from 16 to 4

Abstract

In this work we construct an embedding of a nontrivial central extension of the contact superconformal algebra K'(4) into the Lie superalgebra of pseudodifferential symbols on the supercircle S^{1|2}. Associated with this embedding is a one-parameter family of spinor-like tiny irreducible representations of K'(4) realized just on 4 fields instead of the usual 16.