Deforming the Lie Superalgebra of Contact Vector Fields on $S^{1|1}$

TL;DR

This paper classifies deformations of the Lie superalgebra of contact vector fields on a supercircle, revealing how central charges are affected by superpseudodifferential operators.

Contribution

It provides a classification of nontrivial deformations of the embedding of K(1) into superpseudodifferential operators, linking to central charge deformations.

Findings

Identified all nontrivial deformations of the superalgebra embedding.

Connected deformations to the canonical central extension and superpseudodifferential operators.

Enhanced understanding of the structure of contact vector fields on supercircles.

Abstract

We classify nontrivial deformations of the standard embedding of the Lie superalgebra K(1) of contact vector fields on the (1,1)-dimensional supercircle into the Lie superalgebra of superpseudodifferential operators on the supercircle. This approach leads to the deformations of the central charge induced on K(1) by the canonical central extension of $S\Psi DO$.