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.
Highlights
JHEP07(2018)038 twist operators as a power series in the position of the fourth operator
In the rest of the paper we focus on correlation functions of twist operators only σn1 (z1)σn2 (z2) . . . σns
We argue that in this limit, this kind of correlation functions does not depend on the details of the target space, a property known as universality in the literature [39]
Summary
We begin by reviewing some basic facts about the conformal field theory of the symmetric orbifold. By SN here, we denote the group of permutations This identification introduces new sectors, defined by the boundary conditions. Twist operators are in one-to-one correspondence with the conjugacy classes [g], of the permutation group. Where H(n) denotes the subspace created by a twist operator corresponding to a single-cycle of length n. These symmetric products are of the form. Taking this into account, it is clear that the Hilbert space of the symmetric orbifold CFT can be fully understood once we have constructed the subspace H(n), which we will study in detail
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