DDF operators in the Hybrid Formalism

TL;DR

This paper constructs DDF operators in the hybrid formalism of string theory on AdS3 x S3 x T4, demonstrating they reproduce the entire space-time spectrum and thus derive the dual spectrum from first principles.

Contribution

It introduces a construction of DDF operators within the hybrid formalism, providing a first-principles derivation of the dual space-time spectrum.

Findings

DDF operators reproduce the full space-time spectrum

Construction based on free-field realization of rak{psu}(1,1|2)_1

Derivation of the dual spectrum from first principles

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.