On the Existence of an L$_\infty$ structure for the Super-Virasoro Algebra

TL;DR

This paper explores whether an L_infinity algebra structure can be extended to the super-Virasoro algebra in 2D conformal field theories, focusing on the ${ m N}=1$ case to understand supersymmetric algebra extensions.

Contribution

It investigates the potential extension of L_infinity structures to super-Virasoro algebras, providing insights into supersymmetric algebra frameworks.

Findings

L_infinity structures are examined for super-Virasoro algebra.

Analysis of signs and extensions in supersymmetric algebra structures.

Conclusions on the sufficiency of super-L_infinity algebra extensions.

Abstract

The appearance of L$_\infty$ structures for supersymmetric symmetry algebras in two-dimensional conformal field theories is investigated. Looking at the simplest concrete example of the ${\cal N}=1$ super-Virasoro algebra in detail, we investigate whether an extension to a super-L$_\infty$ algebra is sufficient to capture all appearing signs.