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arXiv · 1804.03207

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

Konstantinos Roumpedakis
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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.

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Konstantinos Roumpedakis. 2018-06-27. Comments on the $S_N$ orbifold CFT in the large $N$-limit. https://doi.org/10.1007/jhep07(2018)038

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