DDF operators in the Hybrid Formalism

Abstract

String theory with one unit of NS-NS flux on ${\text{AdS}}_3\times {\text{S}}^3\times {\mathbb{T}}^4$ has been recently realised to be the exact dual of the symmetric orbifold of ${\mathbb{T}}^4$. In the hybrid formalism of Berkovits, Vafa and Witten and using the free-field realisation of $\mathfrak{psu}(1,1|2{)}_1$, the DDF operators of the free bosons and the free fermions of ${\mathbb{T}}^4$ 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.

arXiv comment32 pages, v2: agrees with the published version

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