Drinfel'd Twisted Superconformal Algebra and Structure of Unbroken Symmetries

TL;DR

This paper studies how Drinfel'd twists deform superconformal symmetries on non(anti)commutative superspaces, classifying all possible twists and analyzing the resulting symmetry breaking and unbroken symmetries.

Contribution

It classifies all abelian twist elements for superconformal algebra and interprets symmetry breaking as modifications of the coproduct due to these twists.

Findings

Classification of all possible abelian twist elements.

Interpretation of symmetry breaking via coproduct modifications.

Analysis of unbroken symmetries in deformed superspaces.

Abstract

We investigate deformed superconformal symmetries on non(anti)commutative (super)spaces from the point of view of the Drinfel'd twisted symmetries. We classify all possible twist elements derived from an abelian subsector of the superconformal algebra. The symmetry breaking caused by the non(anti)commutativity of the (super)spaces is naturally interpreted as the modification of their coproduct emerging from the corresponding twist element. The remaining unbroken symmetries are determined by the commutative properties of those symmetry generators possessing the twist element. We also comment on non-canonically deformed non(anti)commutative superspaces, particularly those derived from the superconformal twist element (\mathcal{F}_{\mathrm{SS}}).