Correlation functions of composite Ramond fields in deformed D1-D5 orbifold SCFT2

On the dynamics of protected ramond ground states in the D1-D5 CFT

“…These integrals are divergent, but can be regularized with the same framework developed in refs. [66][67][68][69]. We show that the regularized integrals of every function (1.3) vanish -a direct verification of the non-renormalization of the generic Ramond ground states.…”

“…we permute all cycles with the same h ∈ S N , ensuring that only disjoint cycles enter the products of twists. This is similar to defining a "normal ordering", see [41,68], which we indicate by writing the composite operator inside square brackets. As we will see later, a prominent rôle will be played by the double-cycle operator with only two twisted strings of lengths n 1 and n 2 , each in its Ramond ground state; it can be expressed explicitly as…”

“…ref. [68]. Note how the definition ensures that the cycles (n 1 ) and (n 2 ) appearing the product are always disjoint.…”

“…From this four-point function one can derive several dynamical data following the same steps as in refs. [66][67][68][69]. Twisted correlators are associated with ramified coverings of the sphere, and their large-N expansion is associated with an expansion in covering surfaces with higher genera [31,33].…”

“…This reduces the problem considerably -in fact, the connected function above has already been considered recently in ref. [68] for Ramond fields with R-charged single-cycle components, for which (1.3) was computed with the stresstensor method. Here we compute (1.3) for all the possible combinations of R-charged and Rneutral single-cycle constituents, by using both the stress-tensor method [30,33,54,70,71] and the Lunin-Mathur covering surface technique [31,32].…”