Deformations of 3-algebras

TL;DR

This paper studies the deformations of 3-algebras and related algebraic structures using cohomology, with a focus on applications to three-dimensional superconformal Chern--Simons theories.

Contribution

It introduces a cohomological framework for analyzing deformations of n-Leibniz and n-Lie algebras, especially for n=3, relevant to theoretical physics.

Findings

Cohomology characterizes algebra deformations

Deformation theory applied to 3-algebras in physics

Framework extends to metric and superconformal cases

Abstract

We phrase deformations of n-Leibniz algebras in terms of the cohomology theory of the associated Leibniz algebra. We do the same for n-Lie algebras and for the metric versions of n-Leibniz and n-Lie algebras. We place particular emphasis on the case of n=3 and explore the deformations of 3-algebras of relevance to three-dimensional superconformal Chern--Simons theories with matter.