Abstract
The symmetric orbifold of 𝕋4 was recently shown to be exactly dual to string theory on AdS3 × S3 × 𝕋4 with minimal (k = 1) NS-NS flux. The worldsheet theory is best formulated in terms of the hybrid formalism of Berkovits, Vafa & Witten (BVW), in terms of which the AdS3 × S3 factor is described by a \( \mathfrak{psu} \)(1, 1|2)k WZW model. At level k = 1, \( \mathfrak{psu} \)(1, 1 2)1 has a free field realisation that is obtained from that of \( \mathfrak{u} \)(1, 1 2)1 upon setting a \( \mathfrak{u} \)(1) field, often called Z, to zero. We show that the free field version of the \( \mathcal{N} \) = 2 generators of BVW (whose cohomology defines the physical states) does not give rise to an \( \mathcal{N} \) = 2 algebra, but is rather contaminated by terms proportional to the Z-field. We also show how to overcome this problem by introducing additional ghost fields that implement the quotienting by Z.
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Gaberdiel, M.R., Naderi, K. & Sriprachyakul, V. The free field realisation of the BVW string. J. High Energ. Phys. 2022, 274 (2022). https://doi.org/10.1007/JHEP08(2022)274
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DOI: https://doi.org/10.1007/JHEP08(2022)274