DDF operators in the hybrid formalism

Abstract

Abstract String theory with one unit of NS-NS flux on AdS3 × S3 × 𝕋4 has been recently realised to be the exact dual of the symmetric orbifold of 𝕋4. In the hybrid formalism of Berkovits, Vafa and Witten and using the free-field realisation of $$ \mathfrak{psu} $$ psu (1, 1|2)1, the DDF operators of the free bosons and the free fermions of 𝕋4 are constructed. It is shown that these DDF operators reproduce the whole spectrum of the space-time theory on the world-sheet and therefore provide a derivation of the dual spectrum from first-principles.