(Twisted) canonical supermultiplets and their resolutions as open-closed homotopy algebras

TL;DR

This paper explores how certain supersymmetric multiplets can be structured as open-closed homotopy algebras using the pure spinor superfield formalism, revealing new algebraic relationships in supersymmetry theories.

Contribution

It introduces a novel application of open-closed homotopy algebras to supersymmetric multiplets via the pure spinor formalism, extending previous algebraic frameworks.

Findings

Supersymmetric multiplets can be structured as open-closed homotopy algebras.

The formalism associates a canonical multiplet to each supersymmetry algebra.

The study extends existing results on algebraic structures in supersymmetry.

Abstract

We argue that some supersymmetric multiplets can naturally be equipped with the structure of an open-closed homotopy algebra. This structure is readily described through the pure spinor superfield formalism, which in particular associates a canonical multiplet for each choice of supersymmetry algebra. We study the open-closed homotopy algebra associated to (twists of) (resolutions of) the canonical multiplet, and show that it fits into a span of open-closed homotopy algebras, extending results of Cederwall et al. arXiv:2304.01258.