Worldsheet Free Fields, Higher Spin Symmetry and Free ${\cal N}=4$ Super Yang-Mills

Abstract

By using the free field worldsheet realization described by Gaberdiel and Gopakumar recently, we construct the nontrivial lowest generators of the higher spin superalgebra $hs(2,2|4)$. They consist of cubic terms between the bilinears of ambitwistor-like fields. We also obtain the worldsheet description for the findings of Sezgin and Sundell twenty years ago given by the familiar oscillator construction. The first order poles of the operator product expansions (OPEs), between the conformal weight-$1$ generators of Lie superalgebra $PSU(2,2|4)$ and the above conformal weight-$3$ generators of $hs(2,2|4)$, are determined explicitly and the additional generators appear in the worldsheet theory.