Comments on the $S_N$ orbifold CFT in the large $N$-limit

Abstract

We elaborate on various aspects of the conformal field theory of the symmetric orbifold. We collect various results that have appeared in the literature, and we present a coherent picture of the operator content of this CFT, relying on the orbifold extension of the Virasoro algebra. We then focus on the large $N$-limit of this theory, discuss the OPE of two twist operators, and find various selection rules. We review how to calculate four-point functions of twist operators, and we write down the most general four-point function in the covering space for large $N$. We show that it depends on some functions that obey a set of algebraic equations, that resemble the scattering equations. Finally, we provide a recipe on how to calculate correlation functions with insertions of the orbifold Virasoro generators.

arXiv comment27 pages

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Cited by in corpus (20)

• A perturbative CFT dual for pure NS-NS AdS${}_3$ strings
• Free field world-sheet correlators for ${\mathrm{AdS}}_3$
• Correlators of the symmetric product orbifold
• From Symmetric Product CFTs to ${\mathrm{AdS}}_3$
• The OPE of bare twist operators in bosonic $S_N$ orbifold CFTs at large $N$
• BPS Correlators for ${\text{AdS}}_3/{\text{CFT}}_2$
• Universal lifting in the D1-D5 CFT
• Correlation functions of symmetric orbifold from AdS${}_3$ string theory
• Correlation functions of composite Ramond fields in deformed D1-D5 orbifold SCFT${}_2$
• On the Dynamics of Protected Ramond Ground States in the D1-D5 CFT
• Stress-energy tensor correlators from the world-sheet
• Renormalization of Twisted Ramond Fields in D1-D5 SCFT${}_2$
• The large $N$ limit of OPEs in symmetric orbifold CFTs with $\mathcal{N}=(4,4)$ supersymmetry
• Twistor Coverings and Feynman Diagrams
• Fractional Conformal Descendants and Correlators in General 2D $S_N$ Orbifold CFTs at Large $N$
• A localising AdS${}_3$ sigma model
• Larger Twists and Higher $n$-Point Functions with Fractional Conformal Descendants in $S_N$ Orbifold CFTs at Large $N$
• Classical geometry from the tensionless string
• Space-time symmetry from the world-sheet
• Scattering and Strebel graphs