Correlators of the symmetric product orbifold

Abstract

We exploit null vectors of the fractional Virasoro algebra of the symmetric product orbifold to compute correlation functions of twist fields in the large $N$ limit. This yields a new method to derive correlation functions in these orbifold CFTs that is purely based on the symmetry algebra. We explore various generalisations, such as subleading (torus) contributions or correlation functions of other fields than the bare twist fields. We comment on the consequences of our computation for the ${\text{AdS}}_3/{\text{CFT}}_2$ correspondence.

arXiv comment44 pages; published version

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• Higher genus correlators for tensionless ${\mathrm{AdS}}_3$ strings
• A slow review of the AGT correspondence
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• Universal lifting in the D1-D5 CFT
• BPS Correlators for ${\text{AdS}}_3/{\text{CFT}}_2$
• Correlation functions of symmetric orbifold from AdS${}_3$ string theory
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• Stress-energy tensor correlators from the world-sheet
• Renormalization of Twisted Ramond Fields in D1-D5 SCFT${}_2$
• DDF operators in the Hybrid Formalism
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• A localising AdS${}_3$ sigma model
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• Space-time symmetry from the world-sheet
• Gromov-Witten/Hilbert versus AdS3/CFT2 Correspondence
• Lecture notes on strings in AdS${}_3$ from the worldsheet and the AdS${}_3$/CFT${}_2$ duality