The large $ \mathcal{N} $ = 4 superconformal $ \mathcal{W} $ ∞ algebra

Abstract

The most general large $ \mathcal{N} $ = 4 superconformal $ \mathcal{W} $ ∞ algebra, containing in addition to the superconformal algebra one supermultiplet for each integer spin, is analysed in detail. It is found that the $ \mathcal{W} $ ∞ algebra is uniquely determined by the levels of the two su(2) algebras, a conclusion that holds both for the linear and the non-linear case. We also perform various cross-checks of our analysis, and exhibit two different types of truncations in some detail.